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No, it must be a geometric solution but without measuring - only by comparing.
I was thinking something like this:
If one shape fits perfectly inside the other one, then it is easy. Same also if one of the two dimensions are exactly the same (for example if the square is AxA and the rectangle BxC and A=B or A=C, then we compare the other sides only.
If, however, say, A>B and A<C then I guess we put one rug onto the other so that they have one common vertex (say, the lower left vertex) and then what?
We have two rugs, one is square and the other is rectangle.
Can we compare them to find out which one has the larger area, but without measuring their distances?
I believe it is correct - solution please? All I managed to do is that the 4th color has 496-396=100 marbles (so in order to have 4 colors, we must pick 496-100+1=397.
We have an urn with 496 marbles of 4 different colors (we don't know the distribution of the colors). If we randomly pick 397 marbles, it is guaranteed that we pick at least one from each color. What is the minimum number of marbles we need to pick, in order to be able to guarantee that we will have 3 colors?
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