Where should the minute hand point to on the bottom clock?

Key concept: In this series of clocks, each clock shows a pair of hand-readings (the numbers the hour hand and the minute hand point to), and the SUM of that pair follows a fixed arithmetic sequence as you move around the clocks in order (here, clockwise starting from the top-left clock). Once that sequence is found from the clocks where both hands are visible, the required sum for the incomplete clock is read off the sequence, and the missing hand is found by subtracting the visible hand's value from that required sum.

1. Top-left clock: the hands point to 1 and 2, so their sum is 1 + 2 = 3.

2. Top-right clock: the hands point to 2 and 4, so their sum is 2 + 4 = 6.

3. Middle-right clock: the hands point to 4 and 5, so their sum is 4 + 5 = 9.

4. Middle-left clock (the last clock in the clockwise cycle): the hands point to 6 and 9, so their sum is 6 + 9 = 15.

5. Listing the four known sums in clockwise order gives 3, 6, 9, __, 15 — each term is 3 more than the one before it, so the missing sum, for the bottom clock (the fourth position in the cycle), must be 9 + 3 = 12.

6. In the bottom clock, the visible hand already points to 7, so the other hand must point to 12 - 7 = 5 for the total to equal 12.

Cross-check: checking both neighbouring terms confirms this — 9 + 3 = 12 (the value just derived) and 12 + 3 = 15, which matches the middle-left clock exactly, so 12 is indeed the required sum for the bottom clock, and a minute-hand reading of 5 is the value that produces it.

Result: so the minute hand must point to 5.