## Puzzle 94: Number Sandwiches

In this arrangement there is one number sandwiched between the "1" cards, two numbers sandwiched between the "2" cards, but only one number sandwich between the "3" cards.

Is it possible to make a complete sandwich with one number between the "1" cards, two numbers between the "2" cards,

Can you make a complete sandwich with 1, 1, 2, 2, 3, 3, 4, 4? Is there is more than one way to arrange the numbers this time?

Extensions:

It is also possible to make a sandwich using 1s, 2s, 3s, 4s, 5s, 6s and 7s. Can you find an arrangement? How many different solutions are there?

Now that you did the arrangements, can you prove that if this works for 1s, 2s, 3s, 4s, 5s and 1s, 2s, 3s, 4s, 5s, 6s?

Is it possible to make a complete sandwich with one number between the "1" cards, two numbers between the "2" cards,

**and**three numbers between the "3" cards? Is there more than one way to arrange the numbers?Can you make a complete sandwich with 1, 1, 2, 2, 3, 3, 4, 4? Is there is more than one way to arrange the numbers this time?

Extensions:

It is also possible to make a sandwich using 1s, 2s, 3s, 4s, 5s, 6s and 7s. Can you find an arrangement? How many different solutions are there?

Now that you did the arrangements, can you prove that if this works for 1s, 2s, 3s, 4s, 5s and 1s, 2s, 3s, 4s, 5s, 6s?

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