Question 1121027: They are six kids they are celebrating their birthday, they are three boys and three girls, but they are each different ages. The youngest is 1 year old. The sum of the ages of the three girls is the same as the sum of the ages of the three boys. What is the smallest possible total of all six ages?
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! They are six kids they are celebrating their birthday, they are three boys and three girls, but they are each different ages. The youngest is 1 year old. The sum of the ages of the three girls is the same as the sum of the ages of the three boys. What is the smallest possible total of all six ages?
:
How about?
Girls: 1 + 5 + 6 = 12
Boys: 2 + 3 + 7 = 12
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smallest total: 24
:
Edwin is right (as usual), except he should have given the girls' ages as
2, 4, 5
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! The other tutor did not get the smallest total. It's 22, not 24.
If the 6 kids were as young as possible with all different ages,
with the youngest being 1, the kids' ages would be 1 through 6,
1+2+3+4+5+6 = 21. But 3 of them must have the same sum as the
other 3, since the sum of the girls' ages equals the sum of the
boys' ages. So the sum of all 6 must be an even number, so we
can split it in half. So we must change the 6 to 7, so the ages
are 1,2,3,4,5,7, which has even sum 22. That means the sum of
the boys' ages and the sum of the girls' ages are 11 each. For
instance, the boys could have ages 1,3,7 and the girls have ages
2,4,6.
So the smallest possible total of the 6 ages is 22.
Edwin
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