Make numbers 93 using the digits 2, 0, 1, 8

Question

I have a 1 to 100 building challenge with 2, 0, 1, 8, all made but 93 is not made. I need your help!

This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8.

Rules:

Use all four digits exactly once
Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root Parentheses and grouping (e.g. "21") are also allowed
Squaring uses the digit 2 so expressions using multiple twos, like 2222 or 12+8212+82, are not allowed
Multi-digit numbers and decimal points can be used such as 20, 102, .02 but you CANNOT make 30 by combining (2+1)0
Recurring decimals can be used using the '

For example :

.2' = 0.222222.....

.12' = 0.1222222.....

.1'2' = 0.12121212.....

$\begingroup$ Does square root also consume the 2? $\endgroup$
– Tweakimp
Jan 4, 2018 at 15:40 — Tweakimp, Jan 4, 2018 at 15:40

Keelhaul · Accepted Answer · 2018-01-04 16:00:57Z

16

I think this is valid by your rules :

$ .1^{-2} - 8 + 0! $
$= 100 - 8 + 1 $
$ = 93 $

answered Jan 4, 2018 at 16:00

Keelhaul

12.6k35 silver badges91 bronze badges

$\begingroup$ Very nice! How long did it take you to come up with it? $\endgroup$
– Jeff Zeitlin
Jan 4, 2018 at 18:33
$\begingroup$ I can't really tell since I was working in parallel^^. I just figured 10^2 - 8 was 92 and asked myself if I could get rid of the 0 for later use $\endgroup$
– Keelhaul
Jan 4, 2018 at 18:55
1

$\begingroup$ Oh, my god! This is crazy! I've been thinking about it for more than a week, but it didn't work out. But I can finally finish the 2018 Challenge! Thank you very much! $\endgroup$
– heypix
Jan 5, 2018 at 6:21

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Tweakimp · Accepted Answer · 2018-01-04 15:46:10Z

1

I am so close with: $\sqrt{\sqrt{\sqrt{12!}}}+80 \approx 92.16 $

answered Jan 4, 2018 at 15:46

Tweakimp

1,82011 silver badges22 bronze badges

$\begingroup$ Not using factorials or roots, $10^2-8=92$ $\endgroup$
– prog_SAHIL
Jan 4, 2018 at 15:54
1

$\begingroup$ Oh, if only you could use the ceiling function! $\endgroup$
– Jakob Lovern
Jan 5, 2018 at 3:23

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2 Answers 2