Monday, December 25, 2023

Palindromic times

 

 
 
Download Clock, Time, Hour. Royalty-Free Vector Graphic - Pixabay 
 
 
 
 


  1. A time such as 3:59:53 is palindromic, that is, it reads the same forward and backward. in a day starting from 0:00:00 to 23:59:59, there are 660 occasions when the time is palindromic. Among them which of the two is closest?

     

     

    Source: Nobuyuki Yoshigahara

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
09:59:59 and 10:00:01

Lucky Seven

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
(95/247)+(86/13)
 
 
 
 
 

 

Cutting Puzzle

 This lovely puzzle is from professor Tanya Khovanova's blog.

You are given a 5-by-7 rectangle with two corners cut out: A 1-by-1 tile is cut from the bottom left corner, and a 1-by-2 tile is cut out of the top right corner, as in the picture. The task is to cut the resulting shape into two congruent polyominoes.