8 = 6 + 2
6 - 5 = 1
2 = 2 + 0
1 + 8 = 9
We start out with:
= = 8 8 2
+ - 2 6 1
= = 5 2 0
+ + 9 1 9
Obviously, for all four lines to yield a valid equation, one of the first two strips must be flipped over. I'll arbitrarily flip the first one:
+ = 8 8 2
= - 2 6 1
+ = 5 2 0
= + 9 1 9
Now, for the first line to have a valid sum, the simplest approach would be to replace one of the 8s with a 6 (to make 2+6=8). Sure enough, the third strip has a 9 at the bottom (which will become a 6 at the top), so we flip that strip:
+ = 6 8 2
= - 5 6 1
+ = 2 2 0
= + 8 1 9
Now, arrange that first line into an equation:
2 + 6 = 8
1 = 5 - 6
0 + 2 = 2
9 = 8 + 1
That almost look right already, but the second line doesn't work. It could work, since 6-5=1, but we need to rearrange some more.
Since the line that needs correction is the subtraction (the only order-sensitive operation), and only the order of the subtraction needs to change (not the sides of the equation), reversing all of the strips should correct the problem, and not affect the equality of any of the other lines.
Inspection shows that this is the case, and the final answer is:
8 = 6 + 2
6 - 5 = 1
2 = 2 + 0
1 + 8 = 9
Original puzzle by Erich Friedman |
