Problem 15 · 2012 Math Kangaroo
Medium
Logic & Word Problems
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Take four cards and on each one write one of the numbers 2, 5, 7, 12. On the back of each card write one of the following properties: “divisible by 7”, “prime number”, “odd”, “greater than 100” so that the number on the other side does not have this property. Every number and every property is used exactly once. Which number is on the card with the property “greater than 100”?
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Answer: C — 7
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Hint 1 of 3
The property written on a card must be FALSE for the number on that card.
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Hint 2 of 3
Pin down the forced pairings first: which number can sit with 'prime'?
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Hint 3 of 3
Match the most restrictive properties one at a time and see which number is left for 'greater than 100'.
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Approach: forced matching
- Each card's stated property must be false for its own number; the numbers are 2, 5, 7, 12.
- 'Prime' must go on the only non-prime, 12; 'odd' must go on an even number, and with 12 used that leaves 2.
- 'Divisible by 7' must go on a non-multiple of 7, so not 7; only 5 remains for it, leaving 'greater than 100' for the last number 7.
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