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A magic triangle brainteaser

By David, 16 September 2020 Brainteaser

Difficulty: Tricky
A triangle with cirles on each point and on each side.
We’re going to make a magic triangle! Take the numbers 1–6 and arrange them in a triangle with three numbers on each side. Swap them around until the sides all add up to the same number.

One more thing – each side must add up to 10. Can you do it?

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

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Brainteaser hint

There aren’t many ways to make 10 with three different numbers. You could start by finding these sums, and then try to fit them into the triangle

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Brainteaser answer

With the numbers 1–6 and no repeated sums, there are only three ways to make 10:
1 + 3 + 6
1 + 5 + 4
3 + 5 + 2

Though the numbers in each sum may appear in a different order, these must be the three sides.

To make a triangle from these sums, note the numbers that appear in more than one sum. Put these odd numbers into the corners, and the even numbers in the middle of each side, in the appropriate spots.

One solution is:
A triangle with circles on each corner and along each side and numbers in each circle.

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  1. The triangle can also be done with the numbers 1, 2, 3, 4, 5 and 7. No typo there, it is possible. See Chapter 4 of Derek Holton’s book Problem Solving: The Creative Side of Mathematics. Paul


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