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India UPSC Exam Fill Odd Numbers in Boxes

A plausible explanation

Here’s a way:
(11-7+9-13) + (1x3x5) + (15) = 30,
where each number is used only “once”.

One clue is to note that you may “repeat” the numbers meaning you most likely need to put more than “1 number” in each box.

Also, the elementary number theory fact that (odd) + (odd) + (odd) = (odd number too) means if we put one “odd number” (odd) in each box we’ll never get an “even” sum of “30” (which is an even number).

This proves definitely that we need to put “more than 1 number” in each box at least once.

Note that we’re given only “odd numbers” as our choice (1,3,5,…15).

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