Puzzle #27: The 3 Matchsticks Heaps

This puzzle is a nice and again a relatively easy one, and the beauty is that children and adults should both enjoy this one. I found this in a puzzle book I bought way back in 1985 – Mathematics can be fun, by Ya. Perelman. There are some other wonderful books by the same author.

When I read the puzzle today morning, I read it wrong, and ended up solving a different puzzle. It so turns out that the original version and the version with my wrong interpretation were both very interesting. So sending both the versions to all of you:

1. A man emptied a box of matches on the table and divided them into three heaps.

“You are not going to start a bonfire, are you?”, someone quipped.

“No, they are for my brain-teaser. Here you are – three uneven heaps. There are altogether 48 matches. I won’t tell how many there are in each heap. If I take as many matches from the first heap as there are in the second and add them to the second, and then take as many from the second as there are in the third and add them to the third, and finally, take as many from the third as there are in the first and add then to the first – well, if I do this, the heaps will all have the same number of matches. How many were there originally in each heap?”


2. Another version of the same question – you take the same steps as above, but find that the three heaps have exactly the same number of matches as what you started with initially.

Enjoy the bonfire!


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2 Responses to Puzzle #27: The 3 Matchsticks Heaps

  1. Tushar Kamat says:

    22, 14 & 12.

  2. DVK says:

    3 15 and 30

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