## TI-84 Plus Silver Edition giveaway puzzle contest

**The contest is over. I've announced the winner here.**

[ Update 11/2. I changed the title of the post to say "TI-84 Plus Silver Edition" rather than "TI-Nspire." ]

No, I'm not reviving Monday Math Madness on a regular basis but Texas Instruments (TI) has offered calculators and t-shirts to readers so I'm going to run a few puzzle contests and give away a prize to the winner of each contest.

Before I announce the contest and rules, here's a word from our sponsor:

STEM skills - science, technology engineering and math - hold the key to tomorrow's innovation. To help students learn tomorrow's job skills, Wild About Math! has teamed-up with Texas Instruments to give away a TI-84 Plus Silver Edition graphing calculator with GraphiTI package. To learn more about TI-84 graphing calculators or other TI products, visit: http://education.ti.com. To learn more about STEM careers, visit: http://education.ti.com/studentzone.

Here's the puzzle. I made it up myself so I don't think searching Google will help you You must solve both parts to be eligible to win:

One can create a triangle of consecutive positive integers as follows:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 . . .Each row, R, has R numbers. Each column, C, has infinitely many numbers. Rows and columns begin at 1. We define a function F(R,C) for row R and column C such that F(R,C) gives us a value in the triangle. Thus, F(1,1) = 1, F(2,1) = 2, and F(2,2) = 3. Note that F(R,C) is only defined when 1 < = C <= R. Part 1: Come up with a formula that computes F(R,C) in terms of R and C for any positive values of R and C when 1 < = C <= R. Show your work. Part 2: Come up with a formula or algorithm that, given a positive integer n, determines R and C.

In order to be eligible to win you must follow the contest rules:

1. Email your answers with solutions to mondaymathmadness at gmail dot com.

2. Only one entry per person.

3. Each person may only win one prize per 12 month period. But, do submit your solutions even if you are not eligible.

4. Your answer must be explained. You must show your work! Wild About Math! will be the final judge on whether an answer was properly explained or not.

5. The deadline to submit answers is Tuesday, November 8, 12:01AM, Pacific Time. (That’s Tuesday morning, not Tuesday night.) Do a Google search for “time California” to know what the current Pacific Time is.)

6. The winner will be chosen randomly from all timely well-explained and correct submissions, using a random number generator.

7. The winner will be announced Friday, November 11, 2010.

8. The winner (or winners) will receive a TI-84 Plus Silver Edition graphing calculator with GraphiTI package.

9. Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.

10. I may post names and website/blog links for people submitting timely correct well-explained solutions. I’m more likely to post your name if your solution is unique.

AsmorNovember 1st, 2010 - 10:11

Minor nitpick, but since F is undefined when C > R, it’s impossible to make a function that works for all positive values of C and R.

SolNovember 1st, 2010 - 10:20

Asmor – Good catch. I’ve updated the problem description. Thanks.

MikeNovember 1st, 2010 - 19:53

Just to clarify: the prize is a TI-84, not an nSpire, right? The post title might be misleading…

cabNovember 2nd, 2010 - 07:00

Can we explain the answer in french? It would be easier for me, but if it’s not possible I’ll make an effort.

SolNovember 2nd, 2010 - 08:12

Mike – You’re right. I screwed up on the title. I’ve just corrected it. Sorry for being misleading.

SolNovember 2nd, 2010 - 08:15

@cab – Go ahead and explain your answer in French. Hopefully there will be enough Math that I can figure out if you got the right answers.

If random.org selects you as the winner and if I can’t tell if your answer is correct or not then I’ll ask you for clarification in English.