money transfers between two banks, no of ways is a power of 2
Source: 9th QEDMO p3 Juniors (21-22. 9. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507
May 15, 2021
number theorycombinatorics
Problem Statement
A numerist has eurodollars and distributes them to two bank accounts in Germany and Switzerland, whereby the Eurodollars cannot be split into smaller monetary units due to the lack of a suitable name. In order to hide all money from the tax authorities if necessary, he would like to be able to move all of his money to account . Due to the immense bureaucracy, money is only allowed to be moved between two accounts if the deposited amount in one account is double. Of course, he can carry out several such transfers in a row. Show that the number of ways to initially distribute the money appropriately is a power of two.