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There are no 4 consecutive integers whose sum is 60. 1+2+3+4=10 2+3+4+5=14 3+4+5+6=18 etc Each step you are adding a number and subtracting a number 4 less than it (eg +5-1, +6-2). So you are adding 4 each time. But 60 does not appear here but 58 and 62 do (sums starting with 13 and 14). Also 60/4=15. so the average of 4 consecutive numbers has to be 15. This average is nowhere odd and so can not be made this way.

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Q: What are 4 consecutive integers whose sum is 60?
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