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

Home > Numbers
Upside Down LCD Display (Posted on 2013-07-15) Difficulty: 3 of 5
In an LCD display some numbers, when viewed upside-down, are images of other numbers. For example, 1995 becomes 5661. The fifth number that can be read upside down is 8, and the 15th is 21, which is 12 when viewed upside-down. What is the millionth number that is meaningful upside-down?

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution (spoiler) | Comment 1 of 2

The number in question are those that contain only 0, 1, 2, 5, 6, 8 and 9--seven distinct digits.

If we use base-7 numbers as a representation of the ordinal positions of the chosen decimal numbers, we can merely take the base-7 version of the ordinal number and translate 3->5, 4->6, 5->8 and 6->9:

ordinal  base-7   translation
1          1           1
2          2           2
3          3           5
4          4           6
5          5           8
6          6           9
7         10          10
8         11          11
9         12          12
10        13          15
11        14          16
12        15          18
13        16          19
14        20          20
15        21          21
16        22          22

This works because the numerical sequence of the number sets correspond to one another, as we just kept the digits in numeric order.

1,000,000 in base-7 is 11333311, so the translation then becomes 11555511, as the millionth number that's meaningful upside-down. It also happens to have the same value upside down.


  Posted by Charlie on 2013-07-15 12:52:44
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 (10)
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