# What a big difference a small change can make

Geometry Level 5

I have three analog clocks. Clock 1 is correct, Clock 2 gains one minute every hour, and Clock 3 loses one minute every hour. I set them all to the correct time at $$12$$ AM. At $$8 \! : \! 20$$ PM, the angle between the hour and minute hands on Clock 1 is $$A^{\circ}$$, the angle between the hour and minute hands on Clock 2 is $$B^{\circ}$$, and the angle between the hour and minute hands on Clock 3 is $$C^{\circ}$$. Assume $$0 \leq A, B, C \leq 180$$. Find the value of $$\left \lfloor A + B + C \right \rfloor$$.

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