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## Magical weights

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Difficulty: Fun

Ellen has a set of 6 weights that come in pairs. One pair is a magical set of negative weights (think helium balloons that take weight away).

2 of the weights are 1 kilogram each, 2 of the weights are 5 kilograms each, and the 2 magical weights are -3 kilograms each.

Ellen tests them out by putting them on a scale. Is it possible for Ellen to weigh out every whole number from 1 to 10?

For example, 2 = 2 x 1 kilogram weights Scroll down or click for a hint, or the answer! ## Brainteaser hint

We recommend getting a pen and paper handy and then writing out the numbers 1 through 10 with each number on its own line. Next, fill in the numbers that are easy like 1, 2 and 5 kilograms.

Here’s the hint: can you find more than one way to make 2 kilograms? This may come in handy for when you need the two 1-kilogram weights, too. Yes, it is possible to make all the numbers between 1 and 10 with Ellen’s weight set. Here are our best answers:

1 = a 1 kilogram weight

2 = a 5 kilogram weight on top of a -3 kilogram weight

3 = one of each weight

4 = 2 x 5 kilogram weights on top of 2 x -3 kilogram weights

5 = a 5 kilogram weight

6 = a 5 kilogram weight plus a 1 kilogram weight

7 = 2 x 5 kilogram weights on top of a -3 kilogram weight

8 = a 1 kilogram and 2 x 5 kilogram weights on top of a -3 kilogram weight

9 = 2 x 1 kilogram and 2 x 5 kilogram weights on top of a -3 kilogram weight

10 = 2 x 5 kilogram weights

Did you find different solutions for any of these calculations? Tell us in the comments!

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