Puzzle of the Day : 45
Speaking Of Children
“We- Aaron, Brian, and Clyde- each have some children.
[1] Aaron has at least one girl and twice as many boys as girls.
[2] Brian has at least one girl and three times as many boys as girls.
[3] Clyde has at least one girl and three more boys than girls.
[4] When I tell you the number of children we have altogether- a number less than 25- you will know how many children I have, but not how many children each of the others has. Altogether we have…”
Who is the speaker?
From [1], Aaron has at least 3 children and a number of children from this sequence:
3,6,9,12,15,18,21,24,…..
From [2], Brian has at least 4 children and a number of children from the sequence:
4,8,12,16,20, 24,……..
From [3], Clyde has at least 5 children and a number of children from this sequence:
5,7,9,11,13,15,17,19,21, 23,….
Then the total number of children is at least 12 and from [4], at most 24. Also: If the total number of children is even, Aaron must have an odd number of children if the total number of children is odd, Aaron must have an even number of children.
Trial and error reveals the following information. The total number of children cannot be 13 because no three numbers numbers, one from each sequence, can total 13. The total cannot be 12, 14, 15, 16, or 17 because then the number of children each had would be known, contradicting [4]. The total cannot be 18,20,21,22,23, or 24 because then no number of children could be known for anybody, contradicting [4]. So the total is 19.
When the total is 19 Aaron must have an even number of children and, from the sequences, this number must not be greater than 19 – (4 + 5) or 10. So Aaron must have 6 children. Then Brian and Clyde together must have 13 children. Then Brian must have either 4 or 8 children. Then: If Brian has 4 children, Clyde has 9 children; if Brian has 8 children, Clyde has 5 children.
So the speaker is Aaron.
Is it Aaron?
Correct!