All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
SOD revealed (Posted on 2021-08-26) Difficulty: 2 of 5
......BTW....SOD IS A HEBREW WORD FOR SECRET!


A dialog between two mathematicians:


Ted: I have two numbers x and y, where x + y = z. The sum of the digits of x is 43 and the sum of the digits of y is 68.
Can you tell me the sum of the digits of z?

Fred: I need more information. When you added x and y how many times did you have to carry?

Ted: Let’s see. … It was five times.
Fred: Then the sum of the digits of z is 66.

Ted: That’s right! How did you know?



How did he know?

Credit: USC mathematician Solomon W. Golomb

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution | Comment 1 of 3
The digital root of the sum x+y equals the sum of the digital roots of a and y.  In fact the sum of the digits will be the same unless there are carries in the addition.  Each carry will reduce this sum by 9.  

So Fred did the following:
43 + 68 = 111
111 - 5*9 = 66.



  Posted by Jer on 2021-08-26 09:11:31
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information