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Puzzles

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Nick's Mathematical Puzzles: 1 to 10. 1. Folded sheet of paper A rectangular sheet of paper is folded so that two diagonally opposite corners come together. If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the shorter side? Hint - Answer - Solution 3. Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. P: I cannot determine the two numbers.S: I knew that.P: Now I can determine them.S: So can I. Given that the above statements are true, what are the two numbers? Answer - Solution 4.

A snug-fitting belt is placed around the Earth's equator. Assume that the Earth is a perfect sphere of radius 6400 km, and that the belt material does not stretch. Hint - Answer - Solution 5. A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. Hint - Answer - Solution 6. Hint - Answer - Solution 7. 9. 10. Undergraduate contest problems and solutions. MathCaching GeoCaching Box #1. A fun card puzzle. I came across a good brain teaser at this site: A pack of cards has 52 cards. You are in a dark room with this pack of cards. You have been told that inside the pack there are 42 cards facing down, 10 cards facing up. You have been asked to reorganize this pack of cards into two decks – so that each deck contains an equal number of cards that face up. This seems like an impossible logic puzzle, but it turns out there is a neat answer. One hint is the two decks do not need to contain an equal number of cards.

A bigger hint If you could see which cards were face up, the puzzle would be trivial. But the puzzle stipulates it’s dark and you cannot determine a card’s orientation. Even though you can’t tell if a card is face up, there is something else you can do. Thus you can move cards to the new deck and you can also choose whether to flip them. The answer Take any ten cards from the original deck. Why is that? Verifying this is a relatively simple counting exercise. NUMB3RS Episode 504: Thirty-Six Hours--Wolfram Research Math Notes.