Sunday, December 24, 2023

An accessible problem from Donald Newman's book

 "A problem Seminar" by Donald J Newman has many excellent problems which require math undergrad/grad knowledge. Below is one of the more accessible problems, solveable by a non-math person.


Each coin is either 10 or 9 grams. Given 4 such coins, find the weight of each using a scale (not a balance, a scale which gives the true weight) no more than 3 times.



Scroll down for a solution.



Suppose the coins are A,B,C,D.

Weigh A+B. It must be 19, otherwise it is trivial. Now weigh A+C. It must be 19, otherwise it is trivial.

Now we must have B=C. Now weigh B+C+D = 2B+D. This has the same parity (odd or even) as D. Thus we know D, which gives us B=C and then A.

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