Yes, you can. Here's an example layout. There appear to be several, as there are some easy ways to rearrange a few tiles. 0 0 0-3 3-3 3-2 | | 2 1 1-1 3 3-5 2 | | 2 2 2-1 1 1-5 2 | | 5 4 4-1 1 5 5-5 | | 5 5-4 4 6 6 0-0 | | 0 4-4 6 6-6 6-0 0-4 4-3 3-6 6-2 - Jason Woolever ------------------------------------------------------ I found many solutions to the Dominos in Connected Groups puzzle from 26 January 2003 update of mathpuzzle.com. Below is the first solution I found: +-+-+-+-+-+-+-+-+ |0 0|0 1|1 1|2 0| +-+-+-+-+-+-+-+-+ |0 3|3 1|1|1 2|2| +-+-+-+-+ +-+-+ + |2 3|3 4|4|1|2|2| +-+-+-+-+-+ + +-+ |3 3|3 6|4|5|5|5| +-+-+-+-+ +-+-+ + |5 3|6 6|4|4 5|5| +-+-+-+-+-+-+-+-+ |5|5 6|6|6 4|4|4| + +-+-+ +-+-+ + + |0|0 6|1|6 2|2|0| +-+-+-+-+-+-+-+-+ Lance Gay ------------------------------------------------------ Fiddled with it for a while. Remembered that you can put seven hexagons on a torus with all of them touching one another. Divided up the 7 x 8 box to emulate that. Fiddled some more so that it could actually be covered with dominoes. _________________________________ | | | | | | | 4 - 0 | 0 | 2 | 2 - 4 | 4 - 4 | |_______| | |_______|_______| | | | | | | | | | 4 - 3 | 3 | 3 | 2 | 4 | 1 | 4 | |_______|___|___| | | | | | | | | | | | | | 3 - 3 | 3 | 2 | 2 | 6 | 1 | 1 | |_______| | |___|___|___|___| | | | | | | | | 3 - 5 | 6 | 6 | 6 | 6 | 1 - 3 | |_______|___|___| | |_______| | | | | | | | 5 - 5 | 6 - 0 | 6 | 1 | 1 - 5 | |_______|_______|___|___|_______| | | | | | | | | 5 | 5 - 6 | 0 - 1 | 1 | 5 | 5 | | |_______|_______| | | | | | | | | | | | 0 | 0 - 0 | 0 - 2 | 2 | 2 | 4 | |___|_______|_______|___|___|___| Warren Phillips ------------------------------------------------------ Thanks. You made me curious as to whether or not this can also be accomplished in a 7x6 rectangle with the doubles removed. This task seems much more difficult. Previously, the doubles added a lot of flexibility. However, after a few days I finally arrived at a solution, if you are interested. The pieces seem to fit together perfectly, with no obvious ways to rearrange them. 6-5 5-3 3-2 2 | 6-3 3 3 0-2 6 | | 4-3 1 0 0-6 6 | 4-1 1-0 0-4 4 2-1 1 0 4 4-2 | | | 6-1 5 5 5 5-2 - Jason ------------------------------------------------------ Here is a better solution. The dominoes themselves all fit in the 7x8 rectangle. The numbered regions are all connected. 2-5 5-1 1-2 2-2 3-5 1-1 0-2 2-3 3-1 1-0 0-3 3-3 3 1 0 0-0 0 4-3 The 3-6, 1-6, 0-6 and 0-4 are vertical 6 6 6 5-0 4 4-6 6-6 5 5-4 4-4 6 The 5-5 and 6-2 are vertical 6-5 5 1-4 4-2 2 Jim Boyce ------------------------------------------------------ Joseph DeVincentis My initial work showed it was easy to fill in the numbers in groups so that they all touched, but hard to do it so you can break it down into a domino set. So I got out the actual dominoes and played with them for a while and eventually came up with this. ------------------------------------------------------