Sunday, May 12, 2024

Dice Game



 























Sorting Numbers

 


 

  1. Arrange the digits 1-9 in a line so that each pair of adjacent digits differs by either 2 or 3.
  2. Arrange the digits 1-9 in a line so that each pair of adjacent digits sums to a prime number.
  3. Now arrange the digits 1-9 in a line so that each pair of adjacent digits (when read as a two-digit number) appears in the times tables from 1 × 1 up to 9 × 9.

 

 

 

        Source: Katie Steckles, The New Scientist

Guess the number

 


Ask a friend to pick a number from 1 through 1000. After asking him 10 questions that can be answered yes or no, you tell them the number. What kind of questions should you ask your friend so that you find their number? 

Source: Kordemsky, The Moscow Puzzles












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.