Question

Using a balance scale and three weights, you can weigh any whole number of pounds from 1 to 13 lb. What are the weights?



a.

1 lb 4 lb 5 lb

c.

1 lb 5 lb 10 lb


b.

1 lb 3 lb 9 lb

d.

2 lb 6 lb 8 lb

Answer 1

Lets say you want to weigh fruits in pounds 1 to 13 pounds using a balance scale.
Now a balance scale has two pans, one pan has the fruit the other pan has weights. but here is the twist, you can add weight to the pan with the fruit in it!

Answer 2

Let the three weights be w, W, and K, where w is the lightest weight,
W is the middle weight, and K is the heaviest weight.

Now clearly the heaviest weight we can weigh is 13,
and this must be when the fruit is in one pan, and all three weights
are in the other pan, so:

w + W + K = 13