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Tom has twelve slips of paper which he wants to put into five cups labeled , , , , . He wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, he wants the five integers to be consecutive and increasing from to . The numbers on the papers are and . If a slip with goes into cup and a slip with goes into cup , then the slip with must go into what cup?

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Mathematical Circles

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Look at this line ” Furthermore, he wants the five integers to be consecutive and increasing from to .” \( \\ \) And then try to find out the values that will be taken by the cups ultimately .

Notice that sum of the numbers in slips is 35 and the average is 7 . Since the numbers are consecutive and increasing from to . So these are 5 , 6 , 7, 8 , and 9 .

Now its a process of elimination . \( \\ \) Like for the cup A : \( \\ \) We have the sum total for cup A is 5 . Now if the slip with 3.5 goes to cup A then there is no slip for the rest 1.5 . As minimum number assigned for the slips is 2 . So the slip with 3.5 can’t go to A . \( \\ \) Proceed similarly for the rest .

- Cup B has a sum of 6, but it has told that it already has a 3 slip, leaving \( 6 -3 =3 \), which is smaller for the 3.5 slip. \( \\ \)

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