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Dice in a Corner

Age 7 to 11
Challenge Level Yellow starYellow starYellow star
Primary curriculum
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Dice in a Corner printable sheet
 
Three dice stacked vertically. The top number is 4, then down the right-hand side are the numbers 2, 1, 1, and down the left-hand side are the numbers 6, 5, 2. Three dice positioned in a line horizontally. The end number on the right is 3, and along the top from left to right are the numbers 1, 5, 5. Along the side from left to right are the numbers 2, 6, 1.
 
Three dice are sitting in the corner with the simple rule that where two faces touch they must be the same numbers. 
So, in the first picture above there are $3$s at the bottom of the red dice and on the top of the middle green and there are $4$s on the bottom of the green dice and the top of the white dice. The numbers on the seven faces that can be seen are then added and make $21$.

In the second picture above there are $4$s at the left of the red dice and on the right of the green dice and there are $3$s on the left of the green dice and the right of the white dice. The numbers on the seven faces that can be seen are then added and make $23$.
 

Use your own dice (you could use two or three or more...)
What total have you made? 
Can you make a different one?
How many different ones can you make?

Now for a challenge - arrange dice (using at least $2$ and up to as many as you like) in a line in the corner, so that the faces you can see add up to $18$ in as many ways as possible.


Each line of dice must be along or up a wall (or two walls). A line going up is counted the same as a line going along. Remember the dice must touch face to face and have the same numbers touching. The dice must be all in one line, so this arrangement below is not allowed:
 An L-shaped arrangement of dice, with two dice stacked top of each other and another dice next to the stack.

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Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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