Feb 27, 2009
What is the color of the cap --- Introduction to modular arithmetic
Hideo Nagahashi
Interpreting 9+5 as 5 hours after 9 am, one could claim 9+5=2 along with usual 9+5=14. The former is known as arithmetic modulo 12. Using arithmetic modulo various numbers, I would like to show some interesting applications to both math itself and daily life. Then I will introduce a nice solution to a variant of famous "prisoners guessing the color of cap to get out of jail" puzzles. (See Math contest Feb problem.) This talk is fairly elementary; knowing usual (not modular!) arithmetic is enough.
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