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# Puzzle

• 29-10-2010 10:49am
Registered Users Posts: 2

Tom and Pat had not met in a number of years but on Tom’s visit to Pat’s new house the following conversation took place ;

Tom : "I am in a great form to-day as I am celebrating my birthday I am 36 years of age"
Pat : "Regarding my 3 children (yes you did not know I am a father) if you multiply the ages of my children you will get 36 also. What are their ages?"
Tom : "Give me additional information to solve the ages of your children"
Pat : "If you sum their 3 ages, the total equals the number on the house next door"
Tom goes out and sees the number on the house next door and comes back into Pat’s house.
Tom : "Still, cannot solve it
I need an additional clue"
Pat : "The girl taking piano lessons is the eldest of the three"
Tom :"I can solve it now
their ages are _, _ and _"
Pat : "Correct"

What are the ages of Pat’s three children?

• Registered Users Posts: 2,534 ✭✭✭

Possible ages (after working out factors of 36):

1, 2, 18 (unlikely age gap)

1, 3, 12

1, 4, 9

2, 2, 9 (two-year-old twins)

2, 3, 6

3, 3, 4 (three-year-old twins)

Given the above information, I don't think it's possible to definitively narrow ages down to one set.

• Registered Users Posts: 3,282 ✭✭✭

Possible ages (after working out factors of 36 -> number in brackets is sum):

1, 1, 36 -> (38)
1, 2, 18 -> (21)
1, 3, 12 -> (16)
1, 4, 9 -> (14)
1, 6, 6 -> (13)
2, 2, 9 -> (13)
2, 3, 6 -> (11)
3, 3, 4 -> (10)

He went outside and looked at the house number and still couldnt tell, that meant the ages could be summed in different ways to make the house number

That rules them all out except for the ones that sum to 13, i.e. if the house was number 10 there was only one answer.

He still didn't know it was 2,2,9 or 1,6,6 until he found out that the "eldest" daughter took piano, that ruled out 1,6,6 as that would mean there was no "eldest"