Forgot to mention the reason :

**(1) Conclusions from "**__The product of their ages is 36.__" :

The ages of the kids can be :

`__AGES__######__SUMS__

1, 1, 36**####x##**38**##x##**[UNIQUE]

1, 2, 18**####x##**21**##x##**[UNIQUE]

1, 3, 12**####x##**16**##x##**[UNIQUE]

1, 4, 9**##x##x##**14**##x##**[UNIQUE]

1, 6, 6**###x#x##**13**##x##**[DUPLICATE]

2, 2, 9**##x##x##**13**##x##**[DUPLICATE]

2, 3, 6**##x##x##**11**##x##**[UNIQUE]

3, 3, 4**##x##x##**10**##x##**[UNIQUE]

**(2) Conclusions from "**__Telling the sum of their ages would not help.__**" :**

As you can see above only we have one pair of duplicates for the sum 13. For all other sums, "Telling the sum of their ages would help" !

So, the kids ages can be 1, 6, 6 or 2, 2, 9.

**(2) Conclusions from "**__The eldest of all is a programmer.__**" :**

Note the use of "The eldest" which means only 1 of them has the max. age.

So, 2, 2, 9 is the required triad of ages.

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Last edited by SaswatPadhi; 21Jun2009 at 17:52..
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