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Maths Problem Puzzle

Maths Problem Puzzle Solution - 19 September

If we have four positive numbers a, b, c and d, there are six ways to multiply the pairs i.e. a*b, a*c, a*d, b*d and c*d. If we tell you the result of five of them without telling you which one is the product of which pair as 2, 3, 4, 5 and 6.

What is the remaining product?

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Solution
2.4

On multiplying all the 6 pairs we get (a*b*c*d)^3.
Assuming the missing product is a*b, then amid the 5 given products we see (a*c)*(b*d)=(a*d)*(b*c)
If we look at the numbers clearly 5 is out of the equation because there is nothing to balance it so the only remaining match is 2*6=3*4, so a*b*c*d=2*6=12.
So the product of all 6 pairs should be 12^3, the product of the given 5 is 720, so the missing one is 12/5=2.4