# Continental Mathematics League (CML) question

1.There are 5 boys who played checkers after school.Each boy played for 4 games of checkers
against each other boys.How many checkers were played altogether?

2.Marcie have 3 sets of light.One set stay lit for 11 seconds and then shuts off for 1 second,the second set stay lit for 7 seconds and shuts off for 1 second and the third set stay lit for 4 seconds and shuts off for 1 second.If the 3 sets are plugged in together beginning the lit cycle,after how many seconds will all three sets of light will be off(Not when they go on altogether.

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(1) Suppose that Boy 1 played $b_1$ games, Boy 2 played $b_2$ games, and so on. Is $$b_1+b_2+b_3+b_4+b_5\tag{1}$$ the total number of games played? Not quite, because each game gets counted twice in $(1)$. For instance, a game between Boy 2 and Boy 3 gets counted once in $b_2$ and once in $b_3$. How should you modify $(1)$ to get a correct figure for the total number of games played?
(2) The lights are off simultaneously precisely when their cycles end simultaneously. The lengths of the cycles for the three lights are $12$ seconds, $8$ seconds, and $5$ seconds. What is the smallest positive integer that is a multiple of $12,8$, and $5$? Once you know that, it’s very easy to figure out when they first all go off simultaneously.