9 distinct positive integers are given, such that the sum of their reciprocals is equal to 1. If 5 of these integers are 3, 7, 9, 11 and 33, and the other 4 integers all have a units digit of 5, what is the sum of these integers?
The five given numbers sum to 491/693 so we need to find four odd multiples of 5 that sum to 202/693.
Four times the smallest unknown integer > 202/693 so s.u.i. < 13 and is therefore 5.
I repeated for the other digits. Instead of calculating each fraction explicitly I found that using a calculator was close enough. At any rate the range of values at any step was limited.
I get the four integers to be 5,15,45,385 which sum with the given integers to 513.
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Posted by xdog
on 2019-04-07 21:12:36 |
solution