This past month The Global Math Project hit the road, joining up with MoMath in New York City to share the joy of math through James Tanton’s Exploding Dots. Over 65 teachers from New York and surrounds, of all backgrounds K -12, played with base machines (including base one-and-half!) making sense of all the standard arithmetic algorithms, and playing with polynomial division, and some infinite series, all with delight and ease.
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Has Exploding Dots made an impact on you or your students? Collecting data on the impact of Exploding Dots is an essential ingredient to our funding efforts. You can help by sharing your own experience of Exploding Dots through our online survey.
We hope you enjoyed the path walking puzzle provided in our last blog. Have a look at our own thinking on that puzzle at the bottom of this post. This week we’ve got a new shareable tidbit of math joy. Check out our Dots Puzzle below. Feel free to share it with others on Facebook.
Thoughts On The
There are multiple ways to solve each of the first two puzzles. The second two puzzles, you might suspect, cannot be solved.
It is easy to prove that something can be done (just do it!) but it is a different matter to prove that something really is impossible. Consider this picture; it has 13 black squares and 12 white squares.
Any path that moves horizontally and vertically from square to square must alternately move from a black square to a white square and from a white square to a black square. We can record a sequence of moves then as a sequence of letters:
B-W-B-W-B-W-B-W-B-W…, or W-B-W-B-W-B-W-B-W-B…
But a sequence starting with the letter W will run out of W’s before it runs out of B’s. (There are only 12 W’s but 13 B’s.) Thus a sequence of moves that starts on a white cell will never be able to reach every cell of the board. As the final two diagrams start on a white cell, there can be no path that fills each board.
CHALLENGE: What can you say about path walking on a 6 x 6 grid of squares? Which cells are permissible starting cells? What about a 6 x 5 grid of squares?
Have fun and share the puzzle with others! Many others! Many many many others!
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