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## 'Sandwiches' printed from http://nrich.maths.org/

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:

Find other solutions with all these digits.