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Multilink Cubes

If you had 36 cubes, what different cuboids could you make?


Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

1, 1, 2, 2, 3, 3
Suppose you have two 1s, two 2s and two 3s. Arrange these six digits in a list so that:
between the two 1s there is one digit, giving 1?1,
between the two 2s there are two digits, giving 2??2, and
between the two 3s there are three digits, giving 3???3.

Can you do the same if you only have 1s and 2s? Explain your answer.

Can you do the same if you include two 4s, and between the two 4s there are four digits?

Here is a solution using 5's, 6's and 7's as well:

7 sandwich

Find other solutions with all these digits.