[Guest]

Three families make a remarkable discovery. The sum of the ages of their members are all the same, the sum of the squares of the ages of their members are all the same, and the sum of the cubes of the ages of their members are all the same. Everyone in all 3 families has a different age, and nobody is more than 100 years old.

What is the smallest possible sum of their ages? Can this be done with 4 families?

[Guest]

1, 10, 100

Edited November 13, 2009 by varin

[Guest]

Here is what I came up with:

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The lowest I had was a sum of 50:

family 1: 10,15,25

family 2: 1,7,18,24

family 3: 3,4,21,22

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The lowest I had was a sum of 94:

family 1: 23,24,47

family 2: 2,14,33,45

family 3: 3,12,35,44

family 4: 5,9,38,42

[superprismatic]

Kevink is correct, at least for 3 families (I only checked that case).

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The maximum sum is 350:

family 1: 75 85 90 100

family 2: 76 82 93 99

family 3: 78 79 96 97

[Guest]

  On 11/13/2009 at 6:31 PM, kevink said:

Here is what I came up with:

  Reveal hidden contents

The lowest I had was a sum of 50:

family 1: 10,15,25

family 2: 1,7,18,24

family 3: 3,4,21,22

  Reveal hidden contents

The lowest I had was a sum of 94:

family 1: 23,24,47

family 2: 2,14,33,45

family 3: 3,12,35,44

family 4: 5,9,38,42

Good job, Kewink.