An ancient balance was found along with 5 weights.
Objects placed on one side of the balance could be counter-balanced by a weight on the other side of the balance to determine the object's weight.
Also, the object and a weight(s) could be placed on one side of the balance and counter balanced to determine its weight, if necessary.
By using only these 5 weights, the ancients were able to determine the weight of objects weighting 1, 2, 3, ..., 120, 121 grams. What are the 5 weights that the archeologists found?
(In reply to
Weights and Scales by delvin)
Way to complicated for my tastes, but I think there are mulitple answers.
first answer
one 1 gram weight
four 30 gram weights
second answer
one 1 gram weight
one 10 gram
one 20 gram
one 40 gram
one 50 gram weight
Logic
one 1 gram weight counters 1 gram object
one 1 gram wt + 1 gram object counters 2 gram object
one 1 gram wt + 2 gram object counters 3 gram object
the four 30 gram wts counters the 120 gram object
or conversely
the 10,20,40,50, grm wts counter the 120 gram object
and just add the one gram weight to the last one to counter the 121 gram object.
the last four weights can be in any amounts so long as the four total 120 grams,
other examples
50,50,10,10 = 120
50,25,25,20 = 120
But one weight must be 1 gram.
re: Weights and Scales
