# Blog

## Sharing beans brainteaser

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Difficulty: Tricky

Abelina and Ben bought a bag of jelly beans, and decided to split it. When they shared the jelly beans out, they split evenly and there wasn’t any remainder.

Before they could pack away the beans, Abelina’s brother Con burst in and asked for a share. Abelina and Ben combined their piles and divided the beans into three equal piles. Once again, the beans divided evenly and there was no remainder.

As soon as they finished, Ben’s family arrived. Daphne, Eric, Fred and Gerry all requested a share. With a sigh, the piles were merged and the beans shared out into seven equal piles. Once again there were no leftover beans.

“I can’t believe we get so few beans,” Abelina complained to Ben. “We started with so many!”

“True,” replied Ben. “But I’m surprised that the beans always split so evenly. It seems like a miracle!”

There were fewer than 50 beans in the bag. Can you work out exactly how many there were?

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

## Brainteaser hint

• Can you find a number that can be divided by 2 and by 3?
• How about 2 and 7?
• How about 3 and 7?
• Now, can you come up with a number that can be divided by 2, 3 and 7?

To find a number that can be divided evenly by 2, 3 and 7, you can multiply those numbers together:
2 x 3 x 7 = 42

Because of the way this answer is calculated, it’s clear you can divide it into two, three or seven equal groups, and it’s less than 50.

To check that 42 is the correct answer, try dividing it out into the correct portions:
• 42 ÷ 2 = 21
• 42 ÷ 3 = 14
• 42 ÷ 7 = 6

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