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# Weird Maths Problem

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Just in case anyone's still curious:

[hide]

All the possible combinations of x + y + z = 13 and their products xyz:

1•1•11 = 11

1•2•10 = 20

1•3•9 = 27

1•4•8 = 32

1•5•7 = 35

1•6•6 = 36

2•2•9 = 36

2•3•8 = 48

2•4•7 = 56

2•5•6 = 42

3•3•7 = 63

3•4•6 = 72

3•5•5 = 75

4•4•5 = 80

All other combinations are commutatively equivalent. Looking back on the list, only one product appears twice. As such, the only way in which the student would need more information is if the number on the study were 36 because otherwise he would be able to figure out the ages based on the product. This is where the tricky part comes in; by saying that his eldest plays the violin, he implies that the ages are 2, 2, and 9 and not 1, 6, and 6 in which case he would have two 'eldest'.[/hide]

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