MathDB

174

Part of 1973 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 174 All Soviet Union MO 1973 14 coins, false and true, weighings

Source:

7/4/2019
Fourteen coins are submitted to the judge. An expert knows, that the coins from number one to seven are false, and from 88 to 1414 -- normal. The judge is sure only that all the true coins have the same weight and all the false coins weights equal each other, but are less then the weight of the true coins. The expert has the scales without weights.
a) The expert wants to prove, that the coins 1−−71--7 are false. How can he do it in three weighings?
b) How can he prove, that the coins 1−−71--7 are false and the coins 8−−148--14 are true in three weighings?
combinatorics