Find out all possible groups of three different numbers that
add up to 13 and arrange them according to given condition.
If one number is 9, it must go with 1 and 3.
If one number is 8, it must go with either 1 and 4 or 2 and 3.
If one number is 7, it must go with either 1 and 5 or 2 and 4.
If one number is 6, it must go with either 2 and 5 or 3 and 4.
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It is clear that 9 must go with 1 and 3. Also, no digit may
be used in more than two sums. Hence, there are 2 cases:
Case I: If 8 goes with 1 and 4, then 7 goes with 2 and 4,
then 6 goes with 2 and 5.
Case II: If 8 goes with 2 and 3, then 7 goes with 2 and 4,
then 6 goes with 3 and 4.
But in case II, 3 is used in three sums. Hence, Case I is
correct. And the possible arrangements are:
9 3 1 5 6 2
8 7
4 7 2 4 8 1
6 3
5 9
Thus, E must be 4.
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