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# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 4, July 2019

2019-06-25

## Gathering Mushrooms

Can you determine how many children gathered mushrooms?

A group of children goes into the forest to gather mushrooms. They take two baskets with them. The larger of the two baskets fits twice as many mushrooms as the smaller basket. First, all of the children gather mushrooms in the larger basket for half an hour. Then, for another half hour, half of the children gather mushrooms in the larger basket and the other half in the smaller basket. After that, all but one child have to go home. This one child collects mushrooms in the smaller basket for another two hours.

Determine how many children collected mushrooms if all of them gathered mushrooms at the same pace and both baskets were full in the end!

## Solution

To solve the puzzle, use the following variables:

• x is the number of children we want to determine.
• n is the number of mushrooms one child collects in half an hour.
• k is the number of mushrooms that fit into the small basket.

The large basket is filled by all of the children for half an hour and then by half of the children for half an hour until it is full. The following equation can be derived from this:

2k = n * x + 1/2 n * x

If you transpose this equation to k/n, you get:

k/n = 3/4 x

The small basket is filled by half of the children for half an hour and then by one child for two hours until it is full. This results in the following equation:

k = 1/2 n * x + 4 n

If you also transpose this equation to k/n, you get:

k/n = 1/2 x + 4

By setting the two equations equal to one another, you get:

3/4 x = 1/2 x + 4

If you solve the equation for x, the result is x = 16. Therefore, a total of 16 kids gathered mushrooms.

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