Spektrum der Wissenschaft, restyled by Amanda Montañez
The hour, minute and second hands of this clock are all the same length and move smoothly in a circle. The dial contains hour and minute markers, but the numbers are missing. Therefore, it’s impossible to tell which one of the 12 hour markers belongs to the 12. The two hands on the left are positioned exactly on hour markers, and the hand on the right is positioned between a minute and an hour marker. What time does the clock show?
Label the lower hand pointing left A, the higher one pointing left C and the one pointing right B. Hands A and C are pointing exactly at hour marks. If one of these two hands is the hour hand, the minute and second hands should both be on top of each other and point at 12. Because this is not the case, B must be the hour hand. Because the minute hand points to a full minute, the second hand must point to 12. There are two possibilities for this. In the first possibility, A is the second hand, and C is the minute hand. Then A is on 12, and C is on 2, and it is 10 minutes past the hour. In that scenario, the hour hand must have traveled 10⁄60 = 1⁄6 of the way from one hour mark to the next. But the picture shows that it has already covered more than 4⁄5 of the distance, so this possibility is ruled out. In the second possibility, C is the second hand, and A is the minute hand, and it is 10 minutes to the hour. The hour hand still has 1⁄6 of its travel from one hour mark to the next, which corresponds to the image. Consequently, the clock shows exactly 4:50:00.
Spektrum der Wissenschaft, restyled by Amanda Montañez
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.
