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Regeneration brainteaser

By David Shaw, 8 June 2023

A sea sponge gets attacked by a shark and is ripped into 100 pieces. Luckily, sea sponges can join back together after they’ve been broken apart. Some pieces form into groups of 7, and the rest form into groups of 29. In the end, there are no pieces left.

How many sponges do we end up with?

Scroll down or click for a hint, or the answer!


 

Brainteaser hint

How many groups of 29 pieces could there be in 100 pieces?

Brainteaser answer

You can work this out by first thinking about the bigger groups of 29! One group of 29 subtracted from 100 would mean 71 pieces are still left. But if they organised into groups of 7, there would be one piece left over.

So you can try the next combination:

2 x 29 = 58

100 – 58 = 42

42 can clump into 6 groups of 7 pieces, with no pieces left over.

There are 2 new sponges made up of 29 pieces, and 6 sponges made up 7 pieces. Together, there are 2 + 6 = 8 sponges.

Thanks to the shark, there’re more sponges now!