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IMP year 1 POW 16: Spiralaterals. POW 16: Spiralaterals Problem Statement:
Spiralaterals-a spiralateral is a sequence of numbers ...
pow 16 spiralaterals. Problem Statement: When there is a sequence of line segments
that forms a spiral-like shape it is known as a spiralateral. ...
POW 16: Spiralaterals. A spiralateral is a series of line segments that form
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Pow #16. Problem Statement : A spiralataral is is a sequence of numbers which
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IMP 2 POW 16 Spiarlaterals. Problem Statement When there is a sequence of line segments
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Submitted by drum boy_01 on February 10, 2007
Category: Miscellaneous
Words: 1342 | Pages: 6
Views: 223
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Linear Nim
Problem Statement:
The game of Linear Nim is a strategy game in which two players take turns removing or eliminating lines or bars from a series of ten lines or bars. There are ten bars or lines in a row on a piece of paper:
l l l l l l l l l l
Each player takes a turn and crosses off one, two, or three of the lines until all of the lines have been crossed off; the person who crosses off the last mark wins.
The question I was trying to answer in this POW is, what is the best strategy for winning this game, i.e. is there one strategy that if followed, will assure that I win the game every time I play it? To decide this, I needed to consider such things as does it matter if one goes first or second to win, and does it matter how many lines get marked off on the first turn, will these make a difference in winning?
To answer the question, the tasks that I needed to do were to play the game several times to see if I noticed any patterns, to write out all of the ways I think might work to help one win, to test those strategies by playing the game again & using them, and then to develop my final strategy and do some variations of it to make sure that my winning strategy truly always works.
Process and Solution:
To answer this question, the first thing I did was to play this game several times with family and friends, looking to see if I noticed any patterns or if I could predict who would win. I started recording the numbers being crossed off and at first it seemed pretty random and puzzling. It didn't seem to matter who went first or how many were marked off on the first turn, but I doubted it was that random or just a matter of luck. After a few more games, I had an "ah-ha" moment: I noticed that if on your turn you made sure that there were four lines left for your opponent, then you were guaranteed to win. I saw that with 4 lines remaining:
If my opponent marked off 1,...
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