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IMO 1994 - Shortlisted problems Question 8

IMO Shortlist · IMO 1994 - Shortlisted problems

Question 8

C3 (MCD) Peter has three accounts in a bank, each with an integral number of dollars. He is only allowed to transfer money from one account to another so that the amount of money in the latter is doubled.
(a) Prove that Peter can always transfer all his money into two accounts.
(b) Can Peter always transfer all his money into one account?