Puzzle Day: Human Jumping Puzzle, Riddle of the Tiled Hearth, and 8 Queens

Today was a fun day in problem-solving. I have been wanting to do the frog jumping puzzle Shaun Carter blogged about since his first post last year. He also made this interactive puzzle shown below:

We did the human jumping puzzle by taking 7 chairs and putting them in a row and making two teams: 3 blue and 3 reds. With AP exams, we happened to have exactly 6 students in class, so it worked perfectly. I recommend that you have students wear a colorful tag because even though they knew who was on each team, I could not keep it straight. The rules are above, but in terms of humans,

• Blue team can only move to their left and red team can only move to their right.
• You can move forward one chair if it is empty and next to you. 
• You can move forward two chairs if you "jump" over someone
• The puzzle is solved when all of the blue team moves to where the red team was and vice versa (order does not matter.

The goal was for my students to do this in as few moves as possible. They did it about 3 times (they are a bright bunch) until they got it right: 15. I wish I took pictures!

We then took away chairs and did it again with 2 blue and 2 reds and also 1 blue and one red and found the pattern to the number of moves it takes, which you can also see on Shaun's post. My students recognized the pattern as perfect squares - 1, starting with (n+1), where n is the number of half the counters (so, only the blue counters, for example.) 

This reminded me of another puzzle, which I read about in this (parentheses), [brackets], and {braces} blog, called The Riddle of the Tiled Hearth. There is a great story that goes along, and we used unifix cubes and played with this for a while. In a nutshell, in a 4x4 grid, you have to place as many of four different tiles (or colors) in the grid without any two colors being in the same row, column, or diagonal...kind of like a type of Sudoku...using the least amount of blank spaces as possible. This took quite some time, and it was interesting how the kids really thought they could do it without having any blank tiles (you can't.) We talked about how tiles had to be "knight moves" away from each other, from chess, so that they were not in the same row, column, or diagonal.

From ppbmath.weebly.com

Then THIS reminded me of ANOTHER puzzle: The Puzzle of the Eight Queens. They loved this one, too...and I did not have an 8x8 sheet ready, but next year I will. The object is to place 8 queens on a chessboard so that none can attack one another...again, none can be in the same row, column, or diagonal. Students could adapt this from the last puzzle by using 8 cubes of one color. The website I linked is cool because students can check their work if you project it on the board and have them tell you their answers.

These were all really fun, and I joked with the kids that they could take the rest of the day off in terms of thinking in the rest of their classes...our heads hurt! Not all of them could solve every problem, but it certainly gave them background info to solve a similar problem in the future.