Only 2 digits ...
What 2 digit number, when read from right to left, is 4 1/2 times as large as when read from left to right?
posted by Zaux at
11:28 AM
Tuesday, March 23, 2010
Links
Search
Share
- Tom Chrome Extension
- ToM @ Twitter
- MeeT ToM
- Daily Tricks Widget
- Vista Gadget 1.5
- iPhone Widget
- Windows XP Widget
- Google Toolbar Button
- Suggestions
Favorite Links
- Vista Sidebar Gadgets
- Widgets for Web 2.0
- C Sharp Tricks
- Interview Information
- Illustrator - Elar Alexander
Bookmark Us
Previous Posts
- The Ransom
- No place like home ...
- Puzzlaria's Rodeo
- The Thief
- Summer Camp
- Number Sets 2
- Number Sets
- Puzzlarian University Reunion
- Another Anchor
- You've got the key ...
5 Comments:
18
Logic: the number cannot be between 20 and 30 as multiplying any number over 20 by 4.5 gives either a 2-digit number beginning with 9 or a 3-digit number which would be wrong, therefore to fit the number would have to end with a 9 (ie would have to be 29) which would give a 3 digit result and is therefore incorrect.
The number cannot be below 10 as it must be 2-digits, and cannot be below 14, as any 2 digit number between 10 and 20 multiplied by 4.5 would give a result beginning with 4 or more so the second digit must be 4 or greater.
The number cannot be odd, as multiplying be 4.5 would give a fractional result.
So narrowing the answer down to an even 2-digit number between 14 and 19 (ie 14, 16 or 18) it was easy to do the maths to come up with 18 / 81.
Hi Dual ...
you are correct.
Let xy be the number. Then want 10y+x = 4.5(10x+y) => 44x = 5.5y
=> 8x = y; so x = 1, y = 8 is the only possibility.
81 is 4.5 * 18
I imagine there exist solutions with n digits (instead of 2) for *some* value. Is there any consistent procedure for finding them?
Post a Comment
Links to this post:
Create a Link
<< Home