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$3b$ | $61-3b$ | Divisible by $4$? |
$3$ | $58$ | no |
$6$ | $55$ | no |
even multiples of $3$ give odd numbers so only try odd multiples of $3$ |
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$9$ | $52$ | yes, $4\times13$; $3$ boys and $13$ girls |
$15$ | $46$ | no |
$21$ | $40$ | yes, $4\times10$; $7$ boys and $10$ girls |
$27$ | $34$ | no |
go up/down in $12$s (multiple of $4$) not $6$s to hit the multiples of $4$ |
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$33$ | $28$ | yes, $4\times7$; $11$ boys and $7$ girls |
$45$ | $16$ | yes, $4\times4$; $15$ boys and $4$ girls |
$57$ | $4$ | yes, $4\times1$; $19$ boys and $1$ girl |