Four weights a+b+c+d=40 kg, find (a,b,c,d) that can weight any object from 1 to 40kg?

a,b,c,d, are four weights that can weight any object from 1 to 40 kgs on an old hand balance

Four weights a+b+c+d=40 kg, find (a,b,c,d) that can weight any object from 1 to 40kg?
Think of this as expressing a number from 1 to 40 in base 3. If you choose the weights to be 1, 3, 9, 27 then you can weigh anything from 1 to 40 by choosing which weights to use (1 + 3 + 9 + 27 = 40). You can put weights ether side to 'subtract' from the value you are trying to form.





So, for example, 11 = 102 base 3. You put the 9 and the three on one side, and the one on the other side 9 + 3 -1 = 11





23 = 212 base 3. So you put the 27 on one side and the 1 and 3 on the other. 27 - 3 - 1 = 23.
Reply:a=32


b=3


c=4


d=1
Reply:This is an old puzzle. Weights of 1, 3, 9, and 27 do it. If something has weight 2, it and the 1 lb, weight will balance the 3 lb, weight. For weight 4, the 3 and the 1 in the other pan will do it. For weight 5, it, the 3, and the 1 will balance the 9. And so on all the way up to 40.





Weights 1, 3, 9, 27, and 81 will go all the way to 121!

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