Resolve this by replacing every pile of two counters by one counter in the column to the left. This is the exploding in #explodingdots. Now we read off the answer in binary. He converted this to decimal 318 and we’re done!

My son was making binary numbers in Lego, so we did a bit of binary adding using a counting board method designed by Napier that’s familiar to him as it’s very like #explodingdots. We started with him setting out some numbers - 8, 12, 3, 33, 76 and 186.

Continued in thread 🧵 #tmwyk

Martin Gardner asks for combinations of four weights 1, 3, 9 and 27 to weigh each of a set of mystery boxes weighing 1-27.

He has you convert the target weight into ternary, then for every 2 you change it to a -1 and add a 1 to the place to the left to it. If 3 is created, replace it with 0 and add 1 to the left. We explored how this works using an #explodingdots machine and realised it’s just the reverse of unexploding dots to deal with isolated anti-dots.

Luke: Look at my Exploding Dots machine! It's a 1 -> 2 -> 3 -> 5 -> 1 machine.
Me: Does it ever stop?
Luke: It has 18 spots.
Me: Oh, so it's done when you fill up the cells?
Luke: Yeah. So if you put one cheerio in, you get two. It's like a +1 function.

#tmwyk #ExplodingDots

When my 7yo was younger we watched some #explodingdots videos: https://youtu.be/KWJVAjONqJM

This has given him such a good understanding of place value and a language to speak about it.

He just read in a history of maths book he picked up at the library that the Babylonians used the same symbol for one and sixty and asked how this worked. I said “they had place value like boxes in an exploding dots machine”. “Oh,” he said, “it’s a 1 to 60 machine, base 60”. So it’s good for history too! #tmwyk

@dhabecker This reminds my of #explodingdots which is also a great way to understand the mechanics behind the algorithms which are usually taught to be blindly followed.

https://twitter.com/Fylwind/status/1043691441359220737

"Classic: 8 dots in a box. A "move" takes two dots in a box and shifts one 1 place left, one 1 place right. Repeat over and over again. Is it obvious this game has to stop? What final configurations of dots are possible? #explodingdots (If you like, this is a base 1 machine!)"