Question 1136106
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Obviously the problem can be solved in many different ways, including trial and error.<br>
Here is a solution that uses only logical reasoning and minimal computation.  It is not an efficient method for finding the answer; but it can be a good exercise in logical reasoning.<br>
(1) The three integers have to be negative, since the product is negative.<br>
(So for the rest of the analysis we can think in terms of positive integers, since it is easier to describe.)<br>
(2) By very rough estimation, the three numbers have to be less than 10.<br>
(3) 5 can't be one of the integers, because the product would have units digit 0.<br>
(4) That leaves only 6*7*8 or 7*8*9 as the possibilities.<br>
(5) Without doing the complete multiplication, 6*7*8 has final digit 6, but 7*8*9 does not; so it has to be 6*7*8.<br>
And then going back to the original problem, where we knew the integers were negative, the three integers are -6, -7, and -8.