Wednesday, September 27, 2017

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


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.....



Answer



I think this is valid by your rules :



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

$= 100 - 8 + 1 $
$ = 93 $



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