Posted by Jimmy on Wednesday, October 10, 2012 at 7:09pm.
Let s be the sum of ten consecutive integers and let p be their product. Explain why the units digit of PS must be 5.

math  Reiny, Wednesday, October 10, 2012 at 8:01pm
In any string of consecutive integers, there must appear a 2, a 5 and a 0,
so the product of any 10 consecutives must end in ...00
let the first of the number be a
The the sum of 10 cosecutives
= (10/2)(2a + 9(1)) = 10a + 45
10a must end in a 0, so subtracting 10 from the product which ends in at least 00 will keep the last digit as a 0
subtracting 45 from last will leave us with a 5 in the unit digit.
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