Inventory of Clocks and Frequency of Chimes

Question

How do you determine the hours for which the clocks chime?

Answer 1

I’ll get you started. In the $90$-minute period from $7$:$15$ to $8$:$45$ the only times at which any of the clocks will chime are $7$:$30$, $8$:$00$, and $8$:$30$.

• At $7$:$30$: Each Type $A$ clock chimes once, the Type $B$ clocks don’t chime, and each Type $C$ clock chimes once, for a total of $10+0+3=13$ chimes.

• At $8$:$00$: Each Type $A$ clock chimes $8$ times, each Type $B$ clock chimes $8$ times, and each Type $C$ clock chimes once, for a total of ... how many chimes?

• At $8$:$30$: This is just like $7$:$30$.