RU-SPB 2012 Problem 112
- Grade 11
We have big multivolume encyclopaedia about dogs on the shelf in alphabetical order, each volume in its specially selected place. Near each place there is an instruction that prescribes one of four actions: to rearrange this volume is one or two places left or right. If you simultaneously run all instructions, volumes will be placed in the same places in another order. The cynologist Dima performs all the instructions every morning. Once he discovered, that the volume of "Bichons" stands still, which was initially occupied by the volume of "Terriers". Prove , that after some time the volume of "Mudies" will stand on the original place of the volume "Poodles".
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.