The current time is between 1 o'clock and 12 o'clock in a wall clock and both the minute hand and the hour hand are situated precisely on two distinct minute marks.

It is observed that the hour hand is precisely a pentagonal number of minute marks ahead of the 12 hour mark. The number of minute marks by which the hour hand is ahead of the minute hand is also a pentagonal number greater than 1.

Determine the current time from the information provided in the above statements.

(In reply to soln, now by Steven Lord)

[EDIT] BUT at 4:12 the hour hand is 21 minute marks  ahead of 12 hour mark, and 21 is NOT a pentagonal number. This violates the first condition in para 2.
 

Edited on January 30, 2022, 4:38 pm

Edited on January 30, 2022, 5:27 pm

Edited on January 30, 2022, 5:28 pm

Edited on January 30, 2022, 5:31 pm

Edited on January 30, 2022, 5:32 pm

Posted by K Sengupta on 2022-01-30 16:34:25