[bushindo]

There are twelve analog clocks (see this pic for image ) on a wall. The clocks are arranged evenly spaced in a circle. None of the clocks is running, however, they are linked in a quirky way. If we forward the time on any clock by x hours, the time on the two clocks on either side of the original clock will go forward by the same x hours. For instance, if the 3 consecutive clocks A, B, and C are currently displaying the time 1:00, 3:00, and 11:00, and we forward clock B by 2 hours, then clock A, B, and C will now display 3:00, 5:00, and 1:00.

Let's say that starting from the very top clock and going clockwise, the clocks are currently displaying the times 4:00, 1:00, 1:00, 2:00, 3:00, 3:00, 4:00, 5:00, 5:00, 6:00, 7:00, 7:00. How much time should we add to each of the 12 clocks so that all 12 hour hands will point straight up, that is, all clocks show the time of precisely 12 o'clock?

[Guest]

Starting from the clock with 4:00 add the following hours: 2 5 4 2 4 3 2 3 2 2 2 1

[bushindo]

Starting from the clock with 4:00 add the following hours: 2 5 4 2 4 3 2 3 2 2 2 1

That was fast. You are correct, good job.

Maybe that was too easy. Here's a bonus question. Cheesner found 1 way to satisfy the puzzle. How many different ways are there to make all 12 clocks display 12:00?

[superprismatic]

add 5 3 3 5 2 2 5 1 1 5 0 0 to the respective clocks.

[superprismatic]

That was fast. You are correct, good job.

Maybe that was too easy. Here's a bonus question. Cheesner found 1 way to satisfy the puzzle. How many different ways are there to make all 12 clocks display 12:00?

144 ways

[bushindo]

144 ways

That's correct. Nicely done!