The parliament of the land of Achronia consists of two houses. The parliament was elected
in 1995 for a period of fours years beginning on Monday, January 1st, 1996, when the two
houses had their first sessions. According to the rules, the meetings of the first house must
occur every ten days for the duration of the term, and the meetings of the second house
must occur every twelve days. For example, the second meetings of the first and the second
houses were held on the 11th and 13th of January respectively.
A new law can be passed only when both houses meet on a Monday.
How many opportunities will the parliament members have to pass new laws
during this four-year term?
The first house meets every 10 days, the second house every 12 days.
They meet simultaneously every 60 days,
. . where 60 is the Least Common Multiple (LCM) of 10 and 12.
They meet together on a Monday every 420 days . . . the LCM of 60 and 7.
Hence, the Monday joint meetings occur on: .
. . during the 4-year (1460-day) term.
Therefore, there are four law-making days.