Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 1, February 2023
Collecting Mushrooms
Can you determine how many children picked mushrooms?
A group of children goes to the forest to pick mushrooms. They take two baskets with them. The larger of the two baskets can hold twice as many mushrooms as the smaller basket. First, all the children collect mushrooms in the larger basket for half an hour. Then half of the children collect mushrooms in the larger basket for another half hour and the other half in the smaller basket. After that, all but one child must go home. This one child continues to pick mushrooms in the smaller basket for another two hours.
Determine how many children collected mushrooms if everyone picked mushrooms at the same pace and both baskets were full at 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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