Re: 1 to 10

On Fri, 30 May 2008, David R Tribble wrote:
aarklon@xxxxxxxxx wrote:

The question is as follows using only four ones write the digits from
1 to 10 the answer is given as follows

William Elliot wrote:
0 = 1 - 1 + 1 - 1
1 = ...

And also:
1 = 1^111

1 = 1^1^1^1

...
16 + (1 + 1 + 1 + 1)!
22 = 11(1 + 1)

Whoops, forgot a few.
110 - 111 - 1
111 = 111*1
112 = 111 + 1

121 = 11*11 = 11^(1 + 1)

1111 = 1111

2048 = (1 + 1)^11
oo = 11^11

Surely that last line is a typo?

Not at all. It's the biggest four 1 number of all. ;-)

How many rational four 1 numbers are there?
Is there an irrational four 1 number? Yes, several.
.1^(1/(1 + 1))
1.1 ^ 1.1

A number is four 1 when it can be expressed by
any number of + - * / ^ . ! and four 1's.

Four 1's can be exactly or atmost. It'll make no difference.

How many four 1 numbers are there?
.

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