.
Al rests on days 4, 8, 12, 16,
and 20. Barb rests on days 8, 9, 10, 18, 19, and 20. They both rest
on days 8 and 20, which is 2 days in each cycle. Thus they have
common rest-days during their first 1000 days.
Al follows a 4-day cycle, and Barb follows a 10-day cycle. The least
common multiple of 4 and 10 is 20. Together they follow a 20-day
cycle, and there are 50 such cycles in 1000 days. Let us number the
days in each cycle as
.
Al rests on days 4, 8, 12, 16,
and 20. Barb rests on days 8, 9, 10, 18, 19, and 20. They both rest
on days 8 and 20, which is 2 days in each cycle. Thus they have
common rest-days during their first 1000 days.
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