Coin Arrangements

Coin Arrangements

Find all the arrangements of heads (H) and tails (T) of n pennies lined up in a row. Record the number of arrangements with 0H, 1H, 2H,…in a table like the following one:

Number of pennies (n)	0H	1H	2H	3H	4H
1
2
3
4

Can you see a pattern to enable you to fill in the table for n = 5,6, etc. ?

2. Repeat problem 1, but this time no two tails can be next to each other.

3. Solve the Towers of Hanoi puzzle for 3 discs and 4 discs. You can use coins of different sizes in place of the disks. Label the disks 1,2,3,4 from smallest to largest. Try to find a pattern to the winning moves that enables you to extend the solution to 5,6,...disks.

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