Mental Floss

Brain Game: Beep Beep


The answer to today's Brain Game may not be as simple as it might appear. Good luck!

At the top of each hour, a digital clock lets out a very quick "beep" once every second to denote the hour. So at one o'clock, the clock beeps once. At two o'clock, it beeps twice, and so on. You note that when it's six o'clock, it takes the device five seconds to sound all its beeps. With this in mind:

How long should it take the clock to sound 12 beeps when it's twelve o'clock?

Here is 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.