Two clocks started and finished ringing simultaneously. The first ones ring every 2 seconds, the second ones - every 3 seconds. In total, 13 strikes were made (coinciding strikes were counted as one). How much time passed between the first and last strikes?
How many times will the clock strike in the first 6 seconds?

## Solution

Within every 6 seconds, the clock strikes 4 times: on the 2nd, 3rd, 4th, and 6th seconds. Therefore, 13 times they will strike when three sets of 6 seconds have passed, plus one more strike, i.e., on the 20th second. Since the first strike occurred on the 2nd second, the pause between the first and last strikes is 18 seconds.

## Answer

$18 \mathrm{s}$.