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
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!