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

Home > Numbers
4 digit number derived from a single digit (Posted on 2018-02-26) Difficulty: 3 of 5
A number consisting of 2 identical digits, say xx
is multiplied by 99.

Write down the product P, given its tens digit (i.e. 3rd from the left) is y.

P&P only.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution Comment 3 of 3 |
P = 121*9*x = 1089 * x

Tens digit (y) from x:

Same as tens digit of 89*x.

But 89*x = (100 - 11) * x and 100*x has zero as tens digit.

So the tens digit is the 9's complement of x, and of course vice versa:

x  y
1  8
2  7
3  6
4  5
5  4
6  3
7  2
8  1
9  0

If y is 8, P must be 1089, etc.:

y   P
8  1089                                                   
7  2178                                                   
6  3267                                                   
5  4356                                                   
4  5445                                                   
3  6534                                                   
2  7623                                                   
1  8712                                                   
0  9801                                                   


  Posted by Charlie on 2018-02-26 12:15:47
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information