Ken Monks
Dept. of Mathematics
University of Scranton
Scranton, PA 18510
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Phone: (570) 941-6101
Fax: (570) 941-5981
Office: STT163-A
 Email: monks@scranton.edu

This page contains the daily tasks for students in Dr. Monks's Math 484 (The Art of Problem Solving) course, Fall term 2010.

Last Training Workout (#26) - Thursday, Dec 2, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• Putnam Practice! Hand in solutions to Zeitz 4.3.13, 4.3.19 (using generating function methods and Maple or a TI-89 to compute the correct coefficient) and the following question.

1. Define the Fibonacci sequence by $$F_0=F_1=1$$ and for all $$n>1$$, $$F_n=F_{n-1}+F_{n-2}$$. Use the method of Generating Functions shown in lecture to derive the closed formula $F_n=\frac{1}{\sqrt{5}}\left(\alpha^{n+1}-\beta^{n+1}\right)$ where $$\alpha=\frac{1+\sqrt{5}}{2}$$ and $$\beta=\frac{1-\sqrt{5}}{2}$$

Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above.

• Problem Training and Must-Know Notebooks

Bring these to class with you on Thursday. I will collect them and grade them while you are practicing Putnam problems, and then hand them back to you before you leave class.

You should send me your last training log spreadsheet before class on Thursday, Dec 9. You should include your hours for the Putnam this Saturday. Note that there is no class on Tuesday, Dec 7, and that class on Thursday Dec 9 starts at 5:15 pm, not 6:00 pm.

• PUTNAM!!!

The 2010 Putnam exam will be held this Saturday, Dec 4, from 10am-1pm and from 3pm-6pm with a two hour break for lunch from 1pm-3pm. The contest will be held in Hyland 102. You should arrive at 9:30am. You should bring pencils, pens, erasers and a watch. Nothing else. Cell phones and music players are prohibited. We will provide you with scrap paper. This is Part I of your final exam in the course. I will explain the details of this in class on Thursday.

Training Workout #25 - Tuesday, Nov 30, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• Read Section 4.3 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

Note that this is the last section we will cover in Zeitz in this course. The remainder of the textbook is essentially his Playbook of problem solving facts and examples from various specific branches of mathematics. This is excellent material to go through on your own slowly in your spare time after the course is over. So carry a copy of Zeitz around with you at all times, and continue your training for the rest of your lives!

• Putnam Practice! Hand in solutions to the following questions.

1. Show that $\sum_{i=1}^n (-1)^{n+i}{n \choose i}{{in} \choose n} = n^n$
2. A white ball has finitely many disk-shaped black regions (closed) painted on its surface. Each black region has area less than half of the surface area of the sphere. No two black regions touch or overlap. Determine, with proof, whether there is always a diameter of the ball with two white endpoints.
3. Show that, if $$n\neq 2$$ is a positive integer, that there are $$n$$ triangular numbers $$a_1,a_2,\ldots,a_n$$ such that $$\displaystyle \sum_{i=1}^n \frac{1}{a_i} = 1$$ (recall that the $$k^{th}$$ triangular number is $$\frac{k(k+1)}{2}$$).

Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above.

Training Workout #24 - Tuesday, Nov 23, 2010

• USAMTS!

Time is up! Hand in your solutions to USAMTS Round One. Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for eight question problem set below.

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• See your name in print!!

Pi Mu Epsilon is a math journal for undergraduates that has a problem section in each issue that undergraduates can solve and submit their solutions to for publication in a future issue. The latest issue has posted its problems here. This is an optional Training Workout task, but if you are interested in trying your hand at a problem and submitting a solution, I will be glad to look at your solution before you submit it to offer feedback (it's not like a contest, so I can tell you if you are right or not). Then you can bring fame to yourself and the University of Scranton Problem Solvers!! Go Fighting Gnomes!!

Training Workout #23 - Thursday, Nov 18, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• Putnam Practice! Hand in solutions to Zeitz 4.1.10 and 4.1.17.

Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the ten and eight question problem set above.

• USAMTS!

Continue working on USAMTS! (Time is running out!)

Training Workout #22 - Tuesday, Nov 16, 2010

• Hand in your answers to the ten question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 13 minutes and 20 seconds with no calculator.

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the same Assignment Answer Form as the ten question set above but write your answers to these eight questions in the second column so that problem number $$n$$ on the eight problem set is written in the answer blank numbered $$n+10$$ on the answer sheet. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• Putnam Practice! Hand in solutions to Zeitz 1.3.13, 3.1.27, 3.2.9, 3.3.24, 3.4.39.

Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the ten and eight question problem set above.

• USAMTS!

Continue working on USAMTS! (Time is running out!)

Training Workout #21 - Tuesday, Nov 9, 2010

• Putnam Practice! Hand in solutions to Zeitz 3.4.19, 3.4.20, 3.4.27, 3.4.32, and the five question set I gave you in class.

• Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above.

• Read Section 4.1 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

• Home Grown Contest - (for Bozo's only)

If you did not already send me two questions for the Home Grown Contest as assigned in Training Workout #19, send them to me asap to avoid another F. Follow the instructions Training Workout #19. If you already sent me them in LyX format, you don't have to do anything else, but you may improve and resubmit your questions if you wish.

• USAMTS!

Continue working on USAMTS! (You never know when someone might ask you about it.)

Training Workout #20 - Thursday, Nov 4, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• USAMTS!

Continue working on USAMTS! (You never know when someone might ask you about it.)

• Putnam Practice! Hand in solutions to the following questions.

• Show that for every collection of nine lattice points (points whose coordinates are all integers) in a three-dimensional Euclidean space there is a lattice point on the interior of at least of the line segments joining two of these points.

• Show that every positive integer is a sum of one or more numbers of the form $$2^r3^s$$ , where $$r$$ and $$s$$ are nonnegative integers and no summand divides another. (For example, $$23 = 9 + 8 + 6$$.)

Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above.

Training Workout #19 - Tuesday, Nov 2, 2010

• Read Section 4.2 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

• Putnam Practice! Hand in solutions to Zeitz 3.3.16, 3.3.19, 3.3.22, 4.2.22, 4.2.23, and 4.2.40.

Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together. Mark the Training Workout Number in the upper right corner of the first page.

• Home Grown Contest!

Go through either my MATHCOUNTS Playbook or my High School Playbook and select at least one fact that you didn't know before [Note: You can use any fact from the MATHCOUNTS Playbook, but only use facts from the High School playbook that are marked with a star symbol.] Then make up two problems, including one that uses the fact you selected (you can pick two facts and make two problems if you like, or use more than one fact in a single problem, but don't make two problems that use the same fact).

Your first problem should be an easy one, perhaps a one to three minute problem, similar to MATHCOUNTS or Problems #1-10 on an AMC. Your second problem should be more challenging, perhaps three to twelve minutes, similar to problems #15-25 on AMC.  It doesn't matter if the hard problem or the easy problem is the one that uses the Playbook fact. You should know how to answer both of your own problems and be ready to explain their solution to the class. The problems should be short-answer format, not multiple-choice (despite what I said in class) and not proof based, i.e. your answers to your questions should be able to fit in the blank on one of our Assignment Answer Forms that you often use for homework.

I will put all of your problems together in random order to form a contest, which we will then take in class, so everyone will get to do everyone else's problem (including the two problems they themselves made up, so everyone should get at least two right!).   The goal is to make good problems.  They should have all of the characteristics of a good problem that we have discussed in the course... interesting, enjoyable, addictive, entertaining, surprising, astonishing, etc.  If they have a messy obvious solution and also a clever solution that uses some Playbook fact, that is great. Messy annoying problems that nobody including you wants to work out will be subject to the wrath and scorn of your peers (author's identities WILL be revealed when you explain your solutions to the class!).  Brilliant enjoyable problems may similarly generate spontaneous laughter and applause!

In order to facilitate my compiling these questions, I ask that you send the two questions to me by email so I can copy and paste your questions into a LyX document. If your question uses math symbols and notation which cannot be typed in email, then I ask that you send it to me directly in LyX file format. LyX is a free math word processor based on LaTeX, and can be downloaded and installed from here. You can email me your two questions as an attachment in .lyx file format (or in the body of the email message if they don't contain any math formatting) any time before class on Nov 2. The subject line of the email message must be "Home Grown Contest - lastname" (without the double quotes and with "lastname" replaced by your last name). The name of your .lyx file attachment should be of the form yourlastname.lyx

In every case you should send me:
• The playbook fact(s) that you used.
• Your solutions to the two questions.

• USAMTS!

Continue working on USAMTS! (You never know when someone might ask you about it.)

Training Workout #18 - Thursday, Oct 27, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• USAMTS!

Continue working on USAMTS! (You never know when someone might ask you about it.)

• Putnam Practice! Hand in solutions to Zeitz 3.3.18 and the following question.

• Prove that there exist integers $$a, b, c$$ not all zero and each of absolute value less than one million such that $\left|a+b\sqrt{2}+c\sqrt{3}\right|<10^{-11}$
Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the thirty question problem set above.

Training Workout #17 - Tuesday, Oct 26, 2010

• Hand in your answers to the thirty question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. If you want to take it under contest conditions time yourself 90 minutes. You can use a calculator, but it isn't needed.

• USAMTS!

Continue working on USAMTS! (You never know when someone might ask you about it.)

• Read Section 3.4 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

• Putnam Practice! Hand in solutions to Zeitz 3.2.8, 3.2.10, 3.2.14, 3.2.15, and the following question.

(Putnam) Find the minimum value of $\frac{(x+1/x)^6-(x^6+1/x^6)-2}{(x+1/x)^3+(x^3+1/x^3)}$ for $$x>0$$

Write up your proofs as you would for the Putnam. Write these on ordinary paper. Do not write more than one solution on a single sheet of paper. Staple all of the pages together, but do not staple it to the answer sheet for the thirty question problem set above.

Training Workout #16 - Thursday, Oct 21, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the new improved Assignment Answer Form. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• USAMTS!

Continue working on USAMTS! (You never know when someone might ask you about it.)

• Read Section 3.3 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

• Putnam Practice! Hand in solutions to Zeitz 3.3.25

Write up a proof as you would for the Putnam. Write these on ordinary paper. If it's more than one page, staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above.

Training Workout #15 - Tuesday, Oct 19, 2010

• Hand in your answers to the fifty question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the new improved Assignment Answer Form. If you want to take it under contest conditions time yourself 120 minutes with no calculator. I don't think they had calculators in 1950.

• USAMTS!

Continue working on USAMTS! (You never know when someone might ask you about it.)

• Read Section 3.2 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

Training Workout #14 - Thursday, Oct 14, 2010

• USAMTS!!!
• Print the USAMTS Year 22, Round 1 problems!
• Read all of the problems now! That will load them into your brain and allow ideas to simmer to the surface.
• Start working on them over break. Don't put these off until the last minute. It will be too late by then.
• Record your progress in your logs as you go. I will expect that you have made substantial progress by the next time we meet and will ask you about it.
• Be patient! Don't give up easily!!

This will be a major consideration in determining your grade in this course, similar to a take-home midterm exam (except that you have six weeks to work on it!) You can use reference books, online math references (that don't involve asking another human being), calculators, Maple, spreadsheets, Geogebra, mechanical models, rulers, protractors, etc. to solve these problems. The only thing you cannot do is discuss the problem with anyone other than me or each other. You can discuss the problems and work with other members of the class as long as for any such collaborative efforts (a) each student writes their own solution and (b) on each problem that you collaborate, mark the name of the people you worked with, and what percentage of the solution was done by you (you should discuss this with your collaborators so the totals add up to 100%). You can also ask me questions to clarify the problem statement, explain Playbook facts, etc.

These five problems will be due on November 22. Note that unless you are still in high school, you should hand these solutions in to me, not submit them to the USAMTS competition. Do not write more than one solution on a single sheet of paper. Neatness counts for this training workout.

Send me an email for each successful solution so I can share in the excitement!

Training Workout #13 - Thursday, Oct 7, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. This is a high school level competition. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• Putnam Practice! Hand in solutions to Zeitz 1.3.10

Write up a proof as you would for the Putnam. Write these on ordinary paper. If it's more than one page, staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above. Do not put more than one problem on the same page.

Training Workout #12 - Tuesday, Oct 5, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. This is a high school level competition. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• Putnam Practice! Hand in solutions to Zeitz 3.1.16, 3.1.17, 3.1.18*, 3.1.20, 3.1.26

Write up a proof as you would for the Putnam. Write these on ordinary paper. If it's more than one page, staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above. Do not put more than one problem on the same page.

*Note that 3.1.18 is not really a problem in our sense of the word, but rather it is a series of questions that are intended to teach you about the theory of symmetric polynomials through hands-on investigation. For part (h) the term cyclic sum is defined on page 71.

Training Workout #11 - Thursday, Sept 30, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. This is a high school level competition. If you want to take it under contest conditions time yourself 40 minutes with no calculator.

• Putnam Practice! Hand in a solution to Zeitz 1.3.14.

Write up a proof as you would for the Putnam. Write these on ordinary paper. If it's more than one page, staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above. Do not put more than one problem on the same page.

Training Workout #10 - Tuesday, Sept 27, 2010

• Hand in your answers to the ten question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. This is a high school level competition. If you want to take it under contest conditions time yourself one hour with no calculator.

• Putnam Practice! Hand in a solution to any three of the following problems from Zeitz 1.3.16, 2.2.13, 2.2.16, and 2.3.32.

Write up a proof as you would for the Putnam. Write these on ordinary paper. If it's more than one page, staple all of the pages together, but do not staple it to the answer sheet for the ten question problem set above. Do not put more than one problem on the same page.

• Register for Math 320 (Chaos and Fractals) for Spring 2011!

OK, that's not really part of the assigned Training Workout, it's just a shameless plug for y'all to register for my course. It meets from 4:00-5:15pm in our same room on Tuesdays and Thursdays. I have a 6:00pm class in the same room, so unfortunately we won't be able to run overtime more than 45 minutes. :( But its a great class anyway, and you are great students, so it's a perfect match! Sign up now! Space is limited!

Training Workout #9 - Thursday, Sept 23, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. This is a high school level competition. If you want to take it under contest conditions time yourself 40 minutes with no calculator. Questions 1-3 are worth 1 point each, questions 4-6 are worth 2 points each, and questions 7-8 are worth 3 points each.

• Putnam Practice! Hand in a solution to Zeitz 2.3.22.

Write up a proof as you would for the Putnam. Write these on ordinary paper. If it's more than one page, staple all of the pages together, but do not staple it to the answer sheet for the eight question problem set above.

There is a wide range of difficulty levels among these problems. Try to force yourself to work on problems that are just beyond your comfort level. Problems that are too easy or too hard don't benefit you much.

Training Workout #8 - Tuesday, Sept 21, 2010

• Hand in your answers to the eight question set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form. This is a high school level competition. If you want to take it under contest conditions time yourself 40 minutes with no calculator. Questions 1-3 are worth 1 point each, questions 4-6 are worth 2 points each, and questions 7-8 are worth 3 points each.

• Hand in solutions to any five of the following problems in Zeitz: 2.4.10, 2.4.12, 2.4.13, 2.4.15, 2.4.19, 2.4.21, 2.4.22, 2.4.23.

Give a short informal proof or explanation for each question, don't just state the answer. Write these on ordinary paper, and staple these solutions together, but do not staple it to the answer sheet for the eight question problem set above. Start each new problem on a separate piece of paper and only write on one side.

Try to find a clever approach that uses either the strategy of drawing a picture, recasting the problem, or changing your point of view. Don't hand in a dumb-ass solution unless it's a last resort.

Note that in problem 2.4.19 the expression $$\lfloor x \rfloor$$ is the greatest integer less than or equal to the real number $$x$$.

There is a wide range of difficulty levels among these problems. Try to force yourself to work on problems that are just beyond your comfort level. Problems that are too easy or too hard don't benefit you much.

• Read the Section 3.1 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

Training Workout #7 - Thursday, Sept 16, 2010

• Hand in your answers to the hexagon problem set I gave you in class.

Hand in your written answers on ordinary paper, and also use the extra copy of the hexagon grid page to enter your answers for those questions. Put your name and Training Workout number at the top right hand corner of your first page and staple (not dog-ear fold) all of your pages (including the hex grid page) together. You should keep the 2-sided question page. You can use the back of the two sided question page for scratch work.

The original contest conditions for this problem were to take it in one hour with a team of four people. If you want to collaborate on this assignment with other people, you may do so, as long as each person does their own write-up, and each person puts the names of all of the other students they collaborated with on their write-ups.

• Read the Section 2.4 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

Training Workout #6 - Tuesday, Sept 13, 2010

• Hand in your answers to the 12 problem set I gave you in class.

If you want to take this problem set under the conditions of the actual contest it came from, give yourself 3 hours. It is scored with 1 point for each correct answer, and 0 points for each incorrect answer. A score of 8 or more is considered to be a good score under these conditions. Show your work in your Problem Solving Notebook.

• Read the Section 2.3 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions.

• Try to solve Problem 13 on the problem set you worked on in class.

You don't have to write up a solution to hand in, but we will discuss solutions at the beginning of class.

Training Workout #5 - Thursday, Sept 9, 2010

• Hand in your answers to the 25 problem set I gave you in class.

If you want to take this problem set under the conditions of the actual contest it came from, give yourself 75 minutes. It was scored with 6 points for each correct answer, 2.5 points for each blank answer, and 0 points for each incorrect answer. A score of 120 is considered to be a good score under these conditions.

• Read the Section 2.2 in Zeitz.

As usual, read it with paper and a pencil in hand, and try the examples before you read his solutions. It's key material in our course, so don't miss it!

• Try to solve 2.1.19, 2.1.21, 2.1.22, and 2.1.23 in Zeitz.

You don't have to write up solutions or hand them in. We will discuss solutions in class.

Training Workout #4 - Tuesday, Sept 7, 2010

• Hand in your answers to the 25 problem set I gave you in class.

If you want to take this problem set under the conditions of the actual contest it came from, give yourself 75 minutes. It was scored with 6 points for each correct answer, 2.5 points for each blank answer, and 0 points for each incorrect answer. A score of 100 is considered to be a good score under these conditions.

• Read the rest of Chapter 1 in Zeitz (you don't have to solve the problems). Also read Section 2.1 in Zeitz.

Read it with paper and a pencil in hand, and try the examples before you read his solutions.  It's GREAT stuff!

Training Workout #3 - Thursday, Sept 2, 2010

• Hand in the 10 problem set I gave you in class.

As usual, you may keep the problems and should hand in your answers on the Assignment Answer Form.

• Read Chapter 1.2 in Zeitz

In particular, read carefully Example 1.2.1. This is a very instructive and enlightening example.

Training Workout #2 - Tuesday, Aug 31, 2010

• Hand in the second set of thirty problems you were given in class.

Note that you should show your work (for problems you don't solve in your head) in your Training Notebook. Write your answers on the official Answer form, and hand that in as discussed in class. Be sure to label it "Training Workout #2" in the upper right hand corner.

• Read the MATHCOUNTS allowable forms of answers page. In particular, you don't want to lose points for a answer that is correct but isn't in the right form.

In particular, if the answer is supposed to be a common fraction, it has to be a reduced fraction, not a mixed number, or a decimal, or a non-reduced fraction. Also for questions where it ask you to find, say, the value of x, if the answer is three, don't write x=3 for your answer... just write 3.

• Read Section 1.1 in the textbook if you haven't already, and try your hand at Example 1.1.3 and 1.1.4 without peeking at the solutions if you have time.  You don't have to hand these in.

Training Workout #1 - Thursday, Aug 26, 2010

• Obtain and organize the following required items for the course. Bring the first two to class with you from now on.

• Problem Training Notebook
Record all of your work for problems that require it in this notebook.
• Must-Know Notebook
This can be a separate notebook or a section in the Problem Training Notebook).
• Training Log
I have posted a sample training log in spreadsheet format here. If you don't have Excel, you can install the free Open Office program and use this version of the Training Log spreadsheet instead. This should not be part of the previous two notebooks, because you have to email it to me before Tuesday's class each week. You can email it any time on Tuesday before 6:00pm, and it should cover everything you did for the problem solving course from Tuesday thru Monday inclusive of the previous week. See the sample spreadsheet for examples.
• Work as many of the 30 problems as you can from the problem set you were given in class. If you want to try it under the timed conditions that the sixth, seventh, and eighth graders have available, give yourself 40 minutes. Then when you are finished, try to answer the ones you didn't finish in time. Calculators are not allowed on these problems.

A few remarks are in order, as this is your first assignment. These remarks will apply to all of your (non-collaborative) problem sets and tasks throughout the semester.

You should not talk to anyone or use the internet to get help on these problems. There is really no point in doing so, because the goal is to develop your ability to solve problems that you do not know how to solve initially, not to get the answers right. So if you feel lost on some problems, that's good. If you feel an urge to ask someone for help, that's just a bad habit from taking previous math courses.

You get no benefit in a jogging class if someone else jogs for you, or if you watch a video of someone jogging on YouTube. Remember that you will not be graded on how many you get correct, but rather if you are training well. For example, you might get some MP awarded if you can explain correctly a clever way that you solved one of these problems. The answers to the problems will be collected. You should keep any scratch work in your Problem Training Notebook.

Hand in just the answers you obtained on this set of problems on the official Assignment Answer Form. Label the form "Training Workout #1" and put your name on it. You can keep the questions. Show your work in your Problem Training Notebook.
• Read: both of the Prefaces in the textbook (pg ix-xiii)
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