Create 10 mathematical expressions equal to 100. Each should use as few instances as possible of a single digit (0 through 9.)

You may use any common operation (+, -, *, /, ^, √, !, [], parentheses, concatenation.)

Lacking the symbols for floor and ceiling (the square brackets [ ]  with the top or bottom part missing),  - I will use the word form: floor(x) (or int(x)) and ceil(x).

Assuming  int(x) is  permited,  100 can be created using only six  zeroes:

5 zeroes   ( int( sqrt ( ( z+z+z)!-1)!))^(z+z),     where z=0!

5 ones:      111-11

5 twos:     (2*2*2+2)^2

5 threes      33*3+3/3   or 4 threes  … if ceil(x) is          permitted :    ceil(33.3*3)    

3 fours        4*4!+4

2 fives       ( int(sqrt 5!)) * (int(sqrt 5!) )

3 sixes       ( int(sqrt (6!/6))) ^ (int(sqrt 6))

4 sevens     (7+7)*7+int(sqrt 7)

3 eights        (8+ int(sqrt8))^( int(sqrt8))

4 nines          99+9/9         

            or 3 nines …   if ceil(x) is  permitted  :    ceil(99.9)   

 

Altogether 39(or 37) ues,   making the generic solution redundant.

 

 

last edition - improved solution

Edited on May 19, 2014, 9:32 am

Posted by Ady TZIDON on 2014-05-18 03:53:04