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Botvid left home between 4 and 5 for a short visit to Amanda

Source: 1995 Swedish Mathematical Competition p2

April 2, 2021
algebraClock

Problem Statement

Botvid left home between 44 and 55 for a short visit to Amanda. When he came back between 55 and 66, he found that the hands of the clock had changed places. What time was it?