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(451) 7

Part of 1995 Tournament Of Towns

Problems(1)

TOT 451 1995 Spring A J7 80 tin cans of provisions

Source:

7/9/2024
A team of geologists on a field expedition have taken with them 8080 tin cans of provisions. The 8080 cans have different weights, which are known (there is a list). After a while the names of the contents of the cans have become illegible. The cook knows what is in each can and claims that he can prove it without opening any can and only using the list and a balance which indicates the difference of weight of the objects placed on its two pans. Show that in order to do so, (a) four weight measurements will be enough, (b) three will not
(AK Tolpygo)
combinatorics