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Deconstructing the Question
Total children = a4a, where a is a digit.
Girls = Boys → total is divisible by 2.
Boys under 13 are twice boys over 13 → boys are in ratio \(2:1\), so the number of boys is divisible by 3.
Key idea: total = 2·(boys), and boys is a multiple of 3 → total must be a multiple of 6.

Step-by-step
Let boys over 13 = \(k\), boys under 13 = \(2k\).
Total boys:
\(k+2k=3k\)
Total children (girls = boys):
\(3k+3k=6k\)
So \(a4a\) must be divisible by 6.

Divisible by 2 → last digit \(a\) is even → \(a\in\{2,4,6,8\}\).
Divisible by 3 → digit sum:
\(a+4+a=2a+4\)
Test:
\(a=4\Rightarrow 2a+4=12\) (multiple of 3), so it works.

Answer: 4
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