Daily Brain Games (Feb 14) - how witty are you?
These are different pentominoes (shapes built up using five squares):
Not all of the possible pentominoes are depicted above: some of them can be mirrored, too.
Your task will be to divide the big rectangle below to pentominoes following these rules:
- The shape of all pentominoes in the rectangle should be DIFFERENT. (Two pentominoes cannot even be mirroring images of each other.)
- The numbers within each pentomino should add up to 10.
Great! You are the winner! :-)))
Congratulations!
I'd love to hear the thought process you went through to reach the solution @doughtaker
The first thing to do is recognize the sets of numbers that you'll be looking for to make pentominoes. These sets are:
5,2,1,1,1 -- 4,3,1,1,1 -- 4,2,2,1,1 -- 3,3,2,1,1 -- 3,2,2,2,1 -- 2,2,2,2,2
with the boldfaced sets being the most important ones for solving this specific problem.
Now look at this picture:
Beginning with the upper left corner, there's a 2 in the corner and a bunch of 1s nearby. It's pretty clear that the only way to place a valid pentomino is if it goes through 2-1-3-1-3 in that order, though exactly which 1s are used are still to be determined at this point. The 2, 3, and 3 are definitely part of the same piece though and can be colored in at this point.
Now in the lower left corner we have a 2 and a diagonally adjacent 5. It's clear that a piece in that area must cover the 5, a single 2, and three 1s. If the piece were to cover the non-corner 2, then the corner 2 would be cut off from the rest of the board and there would be no way to complete the puzzle. Therefore it's known that the corner 2 and the 5 go together as part of one piece, so they can be colored in.
Now in the upper right corner I've put in a reverse C piece to show that it would result in only one possible placement for the pentomino with the nearby 5, and in doing so, it cuts off other squares from the rest of the board and makes it impossible to complete the puzzle. So after a little trial and error, it becomes apparent that there is only one way to fill the right side of the puzzle:
At this point half the puzzle has now been filled in and 5 of the 8 piece locations are fully or partially known. From here, it doesn't take long to finish the rest of the puzzle and get the correct solution.