Dominoes, those little dotted blocks, can make really cool chain reactions. Knock over the first one in a long row, and it knocks over the next one, which topples the next, making a rippling wave. But it takes forever to line them all up on the table. So Matthias Wendel built a clever Lego machine to do it for him. As the gears turn, a Lego arm shoves a domino out onto the table. The rest of the dominoes in the box slide over so the next one is ready. The machine rolls an inch or two, shoves the next domino, and so on. Watch the video to see the machine’s churning gears — and the big domino wave at the end!
Wee ones: What shape is each of those dominoes?
Little kids: If the machine has 5 gears for cranking and 2 wheels with tires for driving, how many wheels does it have in total? Bonus: If the machine could push out the 2nd domino, then the 4th, then the 6th…which number domino would be the 5th domino it pushes out?
Big kids: After the machine lays down 6 rows of dominoes, Matthias has to connect each pair of rows with an arc of 5 dominoes: the 1st row with the 2nd, then the 2nd with the 3rd, on down to the 5th row with the 6th. How many dominoes does Matthias put down by hand? Bonus: If the machine lays down 30 dominoes in each of the 6 rows, how many does it lay?
The sky’s the limit: If each row has 30 dominoes and the machine lays down 20 per batch, after how many dominoes will the machine run empty right at the end of a row?
Wee ones: A rectangle (or rectangular prism, for its 3D shape).
Little kids: 7 wheels. Bonus: The 10th domino (2, 4, 6, 8, 10).
Big kids: 25 dominoes, since he lays 5 connecting arcs (1-2, 2-3, 3-4, 4-5, and 5-6). Bonus: 180 dominoes.
The sky’s the limit: 60 dominoes. We need the lowest number that’s divisible by both 20 and 30. Since both 20 and 30 are divisible by 10, we then just need the first multiple of 10 that’s also divisible by both 2 and 3, giving us 2 x 3 x 10.