One of last week’s puzzles asked how many times per day all six digits on a 24-hour digital clock change simultaneously. Reader **mattcoz **responded, “This one seemed too obvious, my mind wouldn’t accept that it was that easy.” I’m taking this comment as a challenge.

I know why that puzzle played too easy: it was about a *digital* clock. An analog clock, on the other hand, is like *Primer*—those who claim they understand it on first viewing are lying. Think you’re adept at telling time? Prove it by solving this week’s tricky puzzle about a distorted analog clock. If it’s too tough, then blame **mattcoz**. If it’s still too easy, then sundials come next.

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*Did you miss last week’s puzzle? Check it out **here**, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!*

### Puzzle #41: Time Warp

**If you swap the hour hand and the minute hand on an analog clock, how many possible valid times can it still display? **For example, typical clocks sometimes have both hands pointing at the 12 (corresponding to noon) and sometimes have the long hand pointing at the 12 while the short hand points directly at the 6 (corresponding to 6:00), but only the former example will occur on our modified clock—what time would be displayed if you swapped the hands at 6:00? It almost looks like 12:30, but the hour hand should be halfway to the 1.

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Clarifications: The valid times don’t have to be the *correct* time. Ignore AM and PM, just count the number of valid times once around the clock. The hands move continuously (not discretely) around the clock face. The clock has no second hand.

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While we’re futzing with clocks, set your alarms for Monday at 7:30 AM, because I’ll be back with the solution and a new puzzle. Do you know a cool puzzle that you think should be featured here? Message me on X @JackPMurtagh or email me at [email protected]

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### Solution to Puzzle #40: 1% Questions

Shout-out to **MostDispleased** for breaking into the 1% club on last week’s teasers.

Question 1:In the following sequence, what do the letters V and C stand for?V C C C V C C C V C C C C C V C C C C C V C C C C C

The V stands for Vowel and the C for Consonant. There are 26 letters and the Vs are in the same locations as the vowels in the alphabet.

Question 2:On a digital 24-hour clock (military time) that displays hours, minutes, and seconds, how many times in each 24-hour period do all six digits change simultaneously?

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All six digits change simultaneously three times in a 24-hour period: from 09:59:59 to 10:00:00, from 19:59:59 to 20:00:00, and from 23:59:59 to 00:00:00.

Question 3:Jamaica + Japan = 124

Argentina + Armenia = 1245

France + Brazil = 23

England + Germany = ?

56. Jamaica + Japan = 124 because Jamaica and Japan contain the same letters in their first, second, and fourth positions (J, a, and a). France + Brazil = 23 because they have the same letters in their second and third positions (r and a). England and Germany’s letters coincide in their fifth and sixth positions.