SOLUTION: ___/___*___+___*___*___/___+___*___=100 and you can only use 1 thru 9 once.

Algebra ->  Sequences-and-series -> SOLUTION: ___/___*___+___*___*___/___+___*___=100 and you can only use 1 thru 9 once.       Log On


   

Question 354774: ___/___*___+___*___*___/___+___*___=100 and you can only use 1 thru 9 once.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here are all of the ways to generate 100 using the rules given above:


9/2*6+8*7*5/4+3*1 = 100
6/2*9+8*7*5/4+3*1 = 100
9/2*6+7*8*5/4+3*1 = 100
6/2*9+7*8*5/4+3*1 = 100
9/2*6+8*5*7/4+3*1 = 100
6/2*9+8*5*7/4+3*1 = 100
9/2*6+5*8*7/4+3*1 = 100
6/2*9+5*8*7/4+3*1 = 100
9/2*6+7*5*8/4+3*1 = 100
6/2*9+7*5*8/4+3*1 = 100
9/2*6+5*7*8/4+3*1 = 100
6/2*9+5*7*8/4+3*1 = 100
8/4*7+9*6*3/2+5*1 = 100
7/4*8+9*6*3/2+5*1 = 100
8/4*7+6*9*3/2+5*1 = 100
7/4*8+6*9*3/2+5*1 = 100
8/4*7+9*3*6/2+5*1 = 100
7/4*8+9*3*6/2+5*1 = 100
8/4*7+3*9*6/2+5*1 = 100
7/4*8+3*9*6/2+5*1 = 100
8/4*7+6*3*9/2+5*1 = 100
7/4*8+6*3*9/2+5*1 = 100
8/4*7+3*6*9/2+5*1 = 100
7/4*8+3*6*9/2+5*1 = 100
9/3*8+7*5*4/2+6*1 = 100
8/3*9+7*5*4/2+6*1 = 100
9/3*8+5*7*4/2+6*1 = 100
8/3*9+5*7*4/2+6*1 = 100
9/3*8+7*4*5/2+6*1 = 100
8/3*9+7*4*5/2+6*1 = 100
9/3*8+4*7*5/2+6*1 = 100
8/3*9+4*7*5/2+6*1 = 100
9/3*8+5*4*7/2+6*1 = 100
8/3*9+5*4*7/2+6*1 = 100
9/3*8+4*5*7/2+6*1 = 100
8/3*9+4*5*7/2+6*1 = 100
9/2*6+8*7*5/4+1*3 = 100
6/2*9+8*7*5/4+1*3 = 100
9/2*6+7*8*5/4+1*3 = 100
6/2*9+7*8*5/4+1*3 = 100
9/2*6+8*5*7/4+1*3 = 100
6/2*9+8*5*7/4+1*3 = 100
9/2*6+5*8*7/4+1*3 = 100
6/2*9+5*8*7/4+1*3 = 100
9/2*6+7*5*8/4+1*3 = 100
6/2*9+7*5*8/4+1*3 = 100
9/2*6+5*7*8/4+1*3 = 100
6/2*9+5*7*8/4+1*3 = 100
9/6*4+7*5*2/1+8*3 = 100
4/6*9+7*5*2/1+8*3 = 100
9/6*4+5*7*2/1+8*3 = 100
4/6*9+5*7*2/1+8*3 = 100
9/6*4+7*2*5/1+8*3 = 100
4/6*9+7*2*5/1+8*3 = 100
9/6*4+2*7*5/1+8*3 = 100
4/6*9+2*7*5/1+8*3 = 100
9/6*4+5*2*7/1+8*3 = 100
4/6*9+5*2*7/1+8*3 = 100
9/6*4+2*5*7/1+8*3 = 100
4/6*9+2*5*7/1+8*3 = 100
6/8*4+7*5*2/1+9*3 = 100
4/8*6+7*5*2/1+9*3 = 100
6/8*4+5*7*2/1+9*3 = 100
4/8*6+5*7*2/1+9*3 = 100
6/8*4+7*2*5/1+9*3 = 100
4/8*6+7*2*5/1+9*3 = 100
6/8*4+2*7*5/1+9*3 = 100
4/8*6+2*7*5/1+9*3 = 100
6/8*4+5*2*7/1+9*3 = 100
4/8*6+5*2*7/1+9*3 = 100
6/8*4+2*5*7/1+9*3 = 100
4/8*6+2*5*7/1+9*3 = 100
6/2*1+8*7*5/4+9*3 = 100
1/2*6+8*7*5/4+9*3 = 100
6/2*1+7*8*5/4+9*3 = 100
1/2*6+7*8*5/4+9*3 = 100
6/2*1+8*5*7/4+9*3 = 100
1/2*6+8*5*7/4+9*3 = 100
6/2*1+5*8*7/4+9*3 = 100
1/2*6+5*8*7/4+9*3 = 100
6/2*1+7*5*8/4+9*3 = 100
1/2*6+7*5*8/4+9*3 = 100
6/2*1+5*7*8/4+9*3 = 100
1/2*6+5*7*8/4+9*3 = 100
9/1*7+5*3*2/6+8*4 = 100
7/1*9+5*3*2/6+8*4 = 100
9/1*7+3*5*2/6+8*4 = 100
7/1*9+3*5*2/6+8*4 = 100
9/1*7+5*2*3/6+8*4 = 100
7/1*9+5*2*3/6+8*4 = 100
9/1*7+2*5*3/6+8*4 = 100
7/1*9+2*5*3/6+8*4 = 100
9/1*7+3*2*5/6+8*4 = 100
7/1*9+3*2*5/6+8*4 = 100
9/1*7+2*3*5/6+8*4 = 100
7/1*9+2*3*5/6+8*4 = 100
8/4*7+9*6*3/2+1*5 = 100
7/4*8+9*6*3/2+1*5 = 100
8/4*7+6*9*3/2+1*5 = 100
7/4*8+6*9*3/2+1*5 = 100
8/4*7+9*3*6/2+1*5 = 100
7/4*8+9*3*6/2+1*5 = 100
8/4*7+3*9*6/2+1*5 = 100
7/4*8+3*9*6/2+1*5 = 100
8/4*7+6*3*9/2+1*5 = 100
7/4*8+6*3*9/2+1*5 = 100
8/4*7+3*6*9/2+1*5 = 100
7/4*8+3*6*9/2+1*5 = 100
9/3*8+7*5*4/2+1*6 = 100
8/3*9+7*5*4/2+1*6 = 100
9/3*8+5*7*4/2+1*6 = 100
8/3*9+5*7*4/2+1*6 = 100
9/3*8+7*4*5/2+1*6 = 100
8/3*9+7*4*5/2+1*6 = 100
9/3*8+4*7*5/2+1*6 = 100
8/3*9+4*7*5/2+1*6 = 100
9/3*8+5*4*7/2+1*6 = 100
8/3*9+5*4*7/2+1*6 = 100
9/3*8+4*5*7/2+1*6 = 100
8/3*9+4*5*7/2+1*6 = 100
8/1*4+5*3*2/6+9*7 = 100
4/1*8+5*3*2/6+9*7 = 100
8/1*4+3*5*2/6+9*7 = 100
4/1*8+3*5*2/6+9*7 = 100
8/1*4+5*2*3/6+9*7 = 100
4/1*8+5*2*3/6+9*7 = 100
8/1*4+2*5*3/6+9*7 = 100
4/1*8+2*5*3/6+9*7 = 100
8/1*4+3*2*5/6+9*7 = 100
4/1*8+3*2*5/6+9*7 = 100
8/1*4+2*3*5/6+9*7 = 100
4/1*8+2*3*5/6+9*7 = 100
9/6*4+7*5*2/1+3*8 = 100
4/6*9+7*5*2/1+3*8 = 100
9/6*4+5*7*2/1+3*8 = 100
4/6*9+5*7*2/1+3*8 = 100
9/6*4+7*2*5/1+3*8 = 100
4/6*9+7*2*5/1+3*8 = 100
9/6*4+2*7*5/1+3*8 = 100
4/6*9+2*7*5/1+3*8 = 100
9/6*4+5*2*7/1+3*8 = 100
4/6*9+5*2*7/1+3*8 = 100
9/6*4+2*5*7/1+3*8 = 100
4/6*9+2*5*7/1+3*8 = 100
9/1*7+5*3*2/6+4*8 = 100
7/1*9+5*3*2/6+4*8 = 100
9/1*7+3*5*2/6+4*8 = 100
7/1*9+3*5*2/6+4*8 = 100
9/1*7+5*2*3/6+4*8 = 100
7/1*9+5*2*3/6+4*8 = 100
9/1*7+2*5*3/6+4*8 = 100
7/1*9+2*5*3/6+4*8 = 100
9/1*7+3*2*5/6+4*8 = 100
7/1*9+3*2*5/6+4*8 = 100
9/1*7+2*3*5/6+4*8 = 100
7/1*9+2*3*5/6+4*8 = 100
6/8*4+7*5*2/1+3*9 = 100
4/8*6+7*5*2/1+3*9 = 100
6/8*4+5*7*2/1+3*9 = 100
4/8*6+5*7*2/1+3*9 = 100
6/8*4+7*2*5/1+3*9 = 100
4/8*6+7*2*5/1+3*9 = 100
6/8*4+2*7*5/1+3*9 = 100
4/8*6+2*7*5/1+3*9 = 100
6/8*4+5*2*7/1+3*9 = 100
4/8*6+5*2*7/1+3*9 = 100
6/8*4+2*5*7/1+3*9 = 100
4/8*6+2*5*7/1+3*9 = 100
6/2*1+8*7*5/4+3*9 = 100
1/2*6+8*7*5/4+3*9 = 100
6/2*1+7*8*5/4+3*9 = 100
1/2*6+7*8*5/4+3*9 = 100
6/2*1+8*5*7/4+3*9 = 100
1/2*6+8*5*7/4+3*9 = 100
6/2*1+5*8*7/4+3*9 = 100
1/2*6+5*8*7/4+3*9 = 100
6/2*1+7*5*8/4+3*9 = 100
1/2*6+7*5*8/4+3*9 = 100
6/2*1+5*7*8/4+3*9 = 100
1/2*6+5*7*8/4+3*9 = 100
8/1*4+5*3*2/6+7*9 = 100
4/1*8+5*3*2/6+7*9 = 100
8/1*4+3*5*2/6+7*9 = 100
4/1*8+3*5*2/6+7*9 = 100
8/1*4+5*2*3/6+7*9 = 100
4/1*8+5*2*3/6+7*9 = 100
8/1*4+2*5*3/6+7*9 = 100
4/1*8+2*5*3/6+7*9 = 100
8/1*4+3*2*5/6+7*9 = 100
4/1*8+3*2*5/6+7*9 = 100
8/1*4+2*3*5/6+7*9 = 100
4/1*8+2*3*5/6+7*9 = 100

Note: there are 192 ways to do this.