# Ire circum et circum (from smallest to largest)

Which letter should be placed in the last figure? Why?

The letter in the last figure is:

Observations:

The letters around the clock faces spell "day of the week" and, starting with Monday, each letter in the centre occurs in the corresponding day of the week: (M)onday, Tues(D)ay, (W)ednesday, T(H)ursday, Fri(D)ay, Sat(U)rday. It seems likely that one of the letters in "Sunday" goes into the last clock face.

The title is a word-by-word translation of "go round and round" into Latin. "From smallest to largest" does not apply usefully to days of the week. The title might refer to Roman numerals. OP has already made several puzzles about them, they can be ordered from smallest to largest and there are seven different letters used, which line up nicely with the weekdays.

The letter in the middle:

Here's how to get the letter in the middle: Write the name of the day around the clock face, starting with the 1 position. Now imagine that each day can be written around the clock face exactly once, so that the clock for Monday has 6 ticks, the clock for Tuesday has seven ticks and so on.

Now correlate the days of the week with the Roman numerals: I is Monday, V is Tuesday, and so on. Take the letter at the position after counting as many ticks as the Roman numeral's value. Here are the first four days with 1, 5 10 and 50 letters shown:

The position of the letter in the name of the day corresponds to the remainder after dividing by the length of the name. If the remainder is zero, the last letter must be taken. So:

I = 1
V = 5
X = 9 + 1
L = 6 · 8 + 2
C = 16 · 6 + 4
D = 62 · 8 + 4
M = 166 · 6 + 4

We have our letter. it's the fourth letter in "Sunday", D.

• That's it! You got the correct letter, well done! Commented Aug 8 at 11:47