Calculator 11s
Posted: Tue Jan 13, 2009 10:41 am
Apologies if I'm trampling all over Charlie's new subforum with an OT thread, as this isn't strictly a game or a puzzle. But it's an interesting numerical phenomenon which I discovered by accident many years ago and for which I've never been able to find any rationale or explanation. Given the number of maths gurus on this board, one of you may be able to explain why this works the way it does.
OK, here's a thing: imagine you have in your hands a pocket calculator. (That probably gives you some idea of how many years ago it was that I discovered this.) The digits 0-9 are arranged on the keypad like this:
(If you try this on an actual calculator (or a calculator program like the one on Windows) that has the 0 positioned under the 1, you'll need to pretend it's under the 3 for this to work.)
Now, tap in any 4-digit number that conforms to the following rule: Pick a starting digit, and then imagine that digit as being at one corner of a regular 4-sided shape on the keypad. By "regular 4-sided shape", I mean a square, rectangle, parallelogram or rhombus. Tap in the 4-digit number formed by tracking the corners of that shape around the keypad, either clockwise or anticlockwise. For example:
Why?
OK, here's a thing: imagine you have in your hands a pocket calculator. (That probably gives you some idea of how many years ago it was that I discovered this.) The digits 0-9 are arranged on the keypad like this:
Code: Select all
7 8 9
4 5 6
1 2 3
0
Now, tap in any 4-digit number that conforms to the following rule: Pick a starting digit, and then imagine that digit as being at one corner of a regular 4-sided shape on the keypad. By "regular 4-sided shape", I mean a square, rectangle, parallelogram or rhombus. Tap in the 4-digit number formed by tracking the corners of that shape around the keypad, either clockwise or anticlockwise. For example:
- Starting with the 7 and tracing a clockwise square round the outer corners of the main block of 9 digits gives you 7931.
- Starting with the 8, you could trace an anticlockwise parallelogram to give 8129. Also, you can bring the 0 into play by entering 8206.
- Starting with the 5 and working clockwise, you could trace a square to give 5632, or a rhombus to give 5302.
- You can also start with a notional leading 0 to produce a 3-digit number such as (0)341.
Why?