Detailed Solution:

All three stamps could be positioned to fill the shaded hint square. Using Stamps 1 or 2, however, there would be a row which would still need eight shaded squares. Stamp 3 is the only stamp which could fill all eight squares in such a case, but the other rows of squares would not be properly filled. Thus Stamp 3, where its line of four squares are shaded horizontally, must be used.

Working horizontally in the middle tier of blocks, this leaves one square to be shaded in the top row of squares. Thus one block will be shaded by Stamp 1 and the other by Stamp 2 in the orientations shown. If Stamp 2 were to go on the right, subtracting the shaded squares in the right vertical tier of blocks would result in the right-most column of squares needing one more shaded square, which indicates using one copy of Stamp 1 and one copy of Stamp 2. This unfortunately doesn’t work. Stamp 2 must go on the left, with Stamp 1 on the right.

Working vertically in the right tier of blocks, there are simply too many squares which need to be filled to stick with Stamps 1 and 2. There are two possible orientations for Stamp 3 that fit in the right tier, and only one allows for a third stamp in the tier, Stamp 2. Stamp 3 in this orientation cannot go in the bottom-most block, because the row of four shaded squares would sit in a row that can only total two, so Stamp 3 must be in the top block of the tier.

Examining the middle vertical tier and the bottom horizontal tier, it seems that three copies of Stamp 1 and some other stamp in the top left corner must be used to finish the puzzle. The left vertical tier could actually use two of Stamp 2, but we already know it must use one copy of Stamp 1. Trying various orientations of Stamp 1 in the bottom left corner yields a particular orientation of Stamp 3 in the top left corner.

Working horizontally along the bottom tier of blocks, and then vertically along the middle tier of blocks, the final two orientations of Stamp 1 can be determined.

 

 

Last updated: May 26, 2003
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