THE SOLUTION:

Eleven seconds.

The key thing to think about here is that when we say a clock beeps “every second,” what we’re saying is that there’s a one-second gap between beeps. At one o’clock, the device would beep once, but this doesn’t take one second – it only takes a tiny fraction of a second. At two o’clock, when the clock beeps twice, there’s only a one-second gap between the first beep and the second one, so it only takes one second for both beeps to sound. At three o’clock, there’s one second between beeps 1 and 2, and another second between beeps 2 and 3, so it takes two seconds for the clock to sound all three beeps.

Continuing this pattern, at 6 o’clock, it takes five seconds for the clock to sound its six beeps. At 9 o’clock, it takes 8 seconds. And at 12 o’clock, it takes 11 seconds for all 12 beeps to sound.

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