Balance Scale
You wish to weight 40 items that weight from 1 to 40 pounds on a balance scale.
To weigh these you can have four weights of various sizes. Remember you can
put weights on both sides if needed (with the item to weigh on the scales also).
What 4 weights (integer pounds) do you need?
hjg
To weigh these you can have four weights of various sizes. Remember you can
put weights on both sides if needed (with the item to weigh on the scales also).
What 4 weights (integer pounds) do you need?
hjg
Labels: SharedPuzzle
posted by Rajesh Lal at
10:15 PM
6 Comments:
1, 3, 9, and 27. this is because of the formula 1A+3B+9C+27D = N for all integers -40 to 40 where A, B, C, and D are -1, 0 or 1. This is a unique property of the number three, and this pattern continues through the higher powers of three as well.
so an example would be:
34, for example.
(X + 3) V (27 + 9 + 1 )
on the balance.
-3 + 27 + 9 +1 = 34, the weight X is 34.
None.
If there are 40 items, and each item weigh 1 to 40. Then u can just use the scale to “rank” each of the items weights. The lightest item would be 1, and the heaviest item would be 40.
~Cybersurf~
the question is if the 40 items weigh FROM 1-40, meaning there's an item at each weight b/w 1 & 40, then the answer is you only need one weight of 1 lb then find the other 1 lb item and you can get the rest. If not, and all items can weigh anything b/w 1-40, see answer 1 :)
The question posed was what 4 weights would you need. 25#, 10#, 5#, 1#, you could then use the items you found to adjust scales accordingly. Also, it could just be any 4 random weights using cybersurfs theory.
answer 1 does not make sense how can you have a negitive weight to put on a scale.
Answer ONE was completely correct.
There's not a negative weight, the minus meant it was a weight placed on the same side of the scale as the object being weight.
The object weighed X pounds.
27+9+1 was placed opposite the object, making it 37, then 3 pounds added to the side with the object. Now both sides have 37 pounds. The object would then weight X= 37-3 =34.
Congratulation Daniel
Clickety
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