maths puzzle

LewieP

So I have been asked for some help with a maths puzzle by a friend, but can't think of a good way to work it out. Anyone know the answer?

write 1, 2, 3, 4, 5, 6, 7, 8, 9 in that order, fill the gaps with +, -, X, or divided by and make the total 100.

I can't think of a good technique other than trial and error, so if anyone either knows the solution, or how to find it, help would be greatly appreciated

Hlubocky

It would be pretty simple to write a program that enumerates all of the possibilities, since there are only 4^8 combinations. Doing this by hand, you might think about it going backwards. For instance, the last number is nine, so you need to either add 9 to 91, subtract 9 from 109, or divide 900 by 9 (there is no whole number that when multiplied by 9 yields 100). So now your target is 91, 109, or 900. I'm not sure how many solutions there are since I haven't written the program to enumerate all cases, so I'm not sure how likely you are to get a valid answer by working backwards like this.

FunkyWaltDogg

One possible solution:

1 - 2 * 3 + 4 * 5 + 6 + 7 + 8 * 9

With order of operations, that becomes:

1 - (2*3) + (4*5) + 6 + 7 + (8*9)
= 1 - 6 + 20 + 6 + 7 + 72
= 100

EDIT: My answer is wrong if order of operations doesn't apply.

focused7

I'd get 100 with a fewest numbers first then see what combos can cancel the remaining numbers out.

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

I got 100 first then the others added up to 15 and -15 so they canceled each other out.

edit: I assumed you did each operation in a chain and didn't apply order of operations.

LewieP

thanks a bunch guys!