Three Twos
Using three 2s, and only three 2s, how many different numbers can you write? ... and what are they?
posted by Zaux at
6:25 PM
Friday, January 15, 2010
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18 Comments:
This post has been removed by the author.
An infinite number of numbers. They all look like 222, but are written in base n, where n = is any integer > 2.
I'll return to the semantics of your question after sleeping on it.
straight forward question ... no infinite numbers
Chris got one ... 222
I find 4 ways
222
22.2
2.22
.222
Cam
Hi Cam ...no symbols allowed (no decimal) ...
There's 222 which Chris metioned ... and 3 more ... using
2s and only 2s.
on an old calculator 222 upside down looks like 555...
Cam
scratch that last one, that's not right
Cam
these would be easier if you were writing instead of typing ....
2^2^2,22^2,2^22,222 yield 4 different numbers but seems to violate the operator rule
writing one or two of the 2s side ways allows one to write
2 and 22 in different diections (while still using 3 twos)
for 2,22,222 (3 ways)
I strongly anticipate the intended solution will leave me unsatisfied.....
Cam
The intended solution will not leave you unsatisfied unless you are unsatisfied with your solution... that is correct.
If you were writing the numbers, you wouldn't need to use the caret to indicate a power:
222
22²
2²²
²
2²
The small power numbers are actually twos. The last example: 2 to the second power to the second power did not display correctly.
But you had the correct solution.
Couldn't sleep.
So the question should have been written "Using on three 2s and ..."
The way you wrote it made me think you had to use the letters of the phrase.
2 2 2, 2 22, 22 2 and 222. But 'm not been serious now.
Zaux, you've used the mathematical operator 'raised to the power of'. You said that wasn't allowed.
This post has been removed by a blog administrator.
Zaux, at least you put the powers on the right side, on the right (soz Ragknot).
No harm done, let's move on.
In case you didn't know, you can put the superscripted numbers on the left. It's one way of writing the Knuth up arrow operator.
Meh,
I hoped that wasn't the solution.....
Anyhow, moving on.....
Cam
LOL, me too.
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