Wild About Math!

MMM #37: More spiral fun

Our new Monday Math Madness extends the exploration of MMM #36.

Here’s the problem:

Based on the introduction to spiral numbers presented in MMM #36, solve one (or both) of these problems:

1. Come up with an algorithm that tells what number is at an arbitrary X, Y coordinate.
2. Come up with an algorithm that tells the X, Y coordinates for an arbitrary positive integer.

I’ll give three prizes for this contest, one to a random solver as usual, and one each for the best solution to each part of the problem. Even if you’ve won a prize in the last year you’re eligible for one of the “non-random” prizes.

Here are the rules for the contest:

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, July 28, 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, July 31, 2009.
8. The winner (or winners) will receive a Rubik’s Revolution or a $10 gift certificate to Amazon.com or $10 USD via PayPal. For those of you who don’t want a prize I’ll donate $10 to your favorite charity.
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.

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