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Challenging Math Problems

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"Fun and highly formidable math problems and puzzles from noted puzzle creator Terry Stickels." — Window on Resources
Two friends wish to meet for breakfast twice a month throughout the year. In how many ways can they choose those two days so that they never meet on consecutive days?
You want to measure 30 seconds and you have two pieces of string, each of which burns for 40 seconds. How can you accomplish this without bending, folding, or cutting the strings?
A positive whole number is divisi...