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Puzzle Details

At the local BrainBashers Sunday School meeting, the teacher brought in some puppies.

There were 20 more children than puppies.

In the corner of the room, within the ant's nest, the number of ants was 10 times the number of children.

In total, including the teacher, the children, the puppies and the ants, there were 1440 legs in the room.

How many children attended?

With 230 ants (1380 legs), 3 puppies (12 legs) and 1 teacher (2 legs).

If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:

Puppies :             P x 4 =  4P

Children:      (P + 20) x 2 =  2P +   40

Ants    : 10 x (P + 20) x 6 = 60P + 1200

Teacher :                 2 =          2

-----------

66P + 1242

Giving:

66P + 1242 = 1440

66P        = 198

P        = 3

So there were 3 puppies, hence 23 children. QED.

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