Problem 18 · 2009 Math Kangaroo
Stretch
Logic & Word Problems
caseworksum-constraint
Eight cards numbered 1 to 8 are placed in two boxes A and B so that the sum of the cards in each box is the same. If box A holds exactly 3 cards, which of the following statements is definitely true?
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Answer: D — The card numbered 2 is in B.
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Hint 1 of 2
The eight cards add to 36, so each box must total 18.
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Hint 2 of 2
List the 3-card sets that make 18; then see which card lands in the other box every time.
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Approach: check all valid splits
- 1+2+…+8 = 36, so each box sums to 18.
- Box A's three cards summing to 18 can be {3,7,8}, {4,6,8} or {5,6,7}.
- In every one of these, the leftover box B contains the card 2.
- So 'the card numbered 2 is in B' is the statement that is always true — answer D.
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