3 Blocks Towers


Jemima sent us her work on this problem. Well done, Jemima!

I used multilink cubes to make the towers. First of all, I looked for towers that were red at the top. Then I looked for towers that were yellow at the top. Then I looked for towers that were blue at the top. These are the ones I found.

Red, blue, yellowRed, yellow, blueYellow, red, blueYellow, blue, redBlue, red, yellowBlue, yellow, red

Jack from Gosforth Central Middle School explained why only six ways are possible:

With three different colour blocks there are six possible ways of building the tower. This is because for each colour on top there are two options for the other blocks. Therefore as there are three colours to go on top there are $3$ x $2$ options in total, that means six.

David tried the problem with four blocks. Here are the towers he found:


Red, yellow, blue, greenRed, yellow, green, blueRed, blue, yellow, greenRed, blue, green, yellowRed, green, yellow, blueRed, green, blue, yellowYellow, red, blue, greenYellow, red, green, blueYellow, blue, red, greenYellow, blue, green, redYellow, green, red, blueYellow, green, blue, redBlue, red, yellow, greenBlue, red, green, yellowBlue, yellow, red, greenBlue, yellow, green, redBlue, green, red, yellowBlue, green, yellow, redGreen, red, yellow, blueGreen, red, blue, yellowGreen, yellow, red, blueGreen, yellow, blue, redGreen, blue, red, yellowGreen, blue, yellow, red