The numbers and symbols below are placed onto five vertical strips of paper:

           =   =   8   8   2
           +   -   2   6   1
           =   =   5   2   0
           +   +   9   1   9

Rotate and rearrange the strips so that four valid equations appear across the rows.

For example, if you had the 2×1 strips:

=  =  6  6  8
-  +  1  1  5

You could rearrange them as:

5  +  1  =  6
8  =  9  -  1

Note: Consider the numbers as they appear on a digital watch; 0, 1, 2, 5 and 8 are the same when rotated 180°, while 6 and 9 rotate to each other.

To avoid more than one equal sign in a given row and to give each row an equal sign, one or the other of the operation/relation strips must be upside down. They can't be at the end, and they can't be together (to avoid such things as +=, though =+ would be ok if there were enough zeros, as in 02=+2, but, in any case, there are not).

The first (top) row can consist only of 8's, 6's, 2, and/or 1. Out of that, we can get only 6+2=8 or a variation. Since it is on the top and the only minus sign is not on an end, it can't be 8-2=6. The only strip with a 2 at an end is 2109 (read top to bottom); the only one remaining with a six on the end is 6528 (the 8256 inverted), leaving 8621.

The 2 must be next to the 6 with a + between them. As the next line has a 1, 5 and 6 and the = comes between the 1 and the 5, it's the minus sign that comes between the 5 and the 6, and that means the 6 must come before the 5 in the second row, so the first row is 8=6+2. So we get

8=6+2


6-5=1


2=2+0


1+8=9

---------
Note that for the pre to work in these comments, it requires at least one paragraph after its close with a /pre. If such a paragraph is present it should work. The first paragraph after the close of the pre does not wrap and after a certain point you can't see it. That's why I put a short line of hyphens after the close of the pre.

Posted by Charlie on 2003-10-27 09:13:58