Question 107452: ``Two Russian mathematicians meet on a plane.
�If I remember correctly, you have three sons,� says Ivan. �What are their ages today?�
�The product of their ages is thirty-six,� says Igor, �and the sum of their ages is exactly today�s date.�
�I�m sorry, Igor,� Ivan says after a minute, �but that doesn�t tell me the ages of your boys.�
�Oh, I forgot to tell you, my youngest son has red hair.�
�Ah, now it�s clear,� Ivan says. �I now know exactly how old your three sons are.�
How did Ivan figure out the ages?
Found 2 solutions by Edwin McCravy, the_answer_man:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
``Two Russian mathematicians meet on a plane.
“If I remember correctly, you have three sons,” says Ivan. “What are their ages
today?”
“The product of their ages is thirty-six,” says Igor, “and the sum of their
ages is exactly today’s date.”
“I’m sorry, Igor,” Ivan says after a minute, “but that doesn’t tell me the ages
of your boys.”
“Oh, I forgot to tell you, my youngest son has red hair.”
“Ah, now it’s clear,” Ivan says. “I now know exactly how old your three sons
are.”
How did Ivan figure out the ages?
“The product of their ages is thirty-six,”
The only way we can get 3 whole numbers, smallest to largest, such that when
they are all three multiplied together we get 36.
1*1*36 = 36
1*2*18 = 36
1*3*12 = 36
1*4*9 = 36
1*6*6 = 36
2*2*9 = 36
2*3*6 = 36
3*3*4 = 36
“and the sum of their ages is exactly today’s date.”
Now we'll add all those possibilities:
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
This rules out 1,1,36 since 1+1+36 = 38 which is too
big to be today's date, since no month has more than
31 days. So the possibilities are now
1,2,18
1,3,12
1,4,9
1,6,6
2,2,9
2,3,6
3,3,4
"my youngest son has red hair"
This tells us that there IS a youngest son, so that
rules out 2,2,9 and 3,3,4 in which there is no
youngest son because the youngest two are twins, and
thus are the same age.
Ages are 1,2,18, product = 36, sum = 21, date = 21st
Ages are 1,3,12, product = 36, sum = 16, date = 16th
Ages are 1,4,9, product = 36, sum = 14, date = 14th
Ages are 1,6,6, product = 36, sum = 13, date = 13th
Ages are 2,3,6, product = 36, sum = 11, date = 11th
It could be any of those 5 possibilities. Are you sure
you didn't leave something out?
Edwin
Answer by the_answer_man(1)  (Show Source):
You can put this solution on YOUR website! There are eight sets of three numbers whose product is 36. Their sums are as
follows:
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
4 + 3 + 3 = 10
We can immediately rule out (1 + 1 + 36) because it couldn't be a date.
1 + 2 + 18 = 21
1 + 3 + 12 = 16
1 + 4 + 9 = 14
1 + 6 + 6 = 13
2 + 2 + 9 = 13
2 + 3 + 6 = 11
4 + 3 + 3 = 10
Knowing that the sum is today's date wasn't enough to figure out which
possibility it was, so that must mean that day's date has multiple options.
That leaves us with:
1 + 6 + 6 = 13
2 + 2 + 9 = 13
We know that he has a youngest son, so this means the answer is 1, 6, 6.
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