In how many ways is it possible to read the word "MADAM" in the diagram? You may go as you please,
upwards and downwards, forwards and backwards, any way possible along the open paths. But the letters
in every case must be contiguous, and you may never pass a letter without using it.
Solution to the Problem:
The answer is 80 different ways.Many thanks to Keith Mealy and to James Alarie for pointing out that the rules did not prevent you from retracing a path and using the letters over again. Here was my original answer of 30 ways:
But you can double that since you could start from either end of M-A-D-A-M in each of the paths above.
Then there is an additional 5 ways that can be found from each of the four Ms by going out M-A-D and then returning over the same letters. So, 60 + 20 = 80 ways!
James Alarie sent in the results of his computer program where he labeled each of the letters in the diagram clockwise around the outer rim from 1 to 16, then on the next four within 17-20, and the center as 21.
The paths that his program found are:
1 2 3 2 1
1 2 3 4 5
1 2 3 17 1
1 2 3 18 5
1 16 15 14 13
1 16 15 16 1
1 16 15 17 1
1 16 15 20 13
1 17 3 2 1
1 17 3 4 5
1 17 3 17 1
1 17 3 18 5
1 17 15 14 13
1 17 15 16 1
1 17 15 17 1
1 17 15 20 13
1 17 21 17 1
1 17 21 18 5
1 17 21 19 9
1 17 21 20 13
5 4 3 2 1
5 4 3 4 5
5 4 3 17 1
5 4 3 18 5
5 6 7 6 5
5 6 7 8 9
5 6 7 18 5
5 6 7 19 9
5 18 3 2 1
5 18 3 4 5
5 18 3 17 1
5 18 3 18 5
5 18 7 6 5
5 18 7 8 9
5 18 7 18 5
5 18 7 19 9
5 18 21 17 1
5 18 21 18 5
5 18 21 19 9
5 18 21 20 13
9 8 7 6 5
9 8 7 8 9
9 8 7 18 5
9 8 7 19 9
9 10 11 10 9
9 10 11 12 13
9 10 11 19 9
9 10 11 20 13
9 19 7 6 5
9 19 7 8 9
9 19 7 18 5
9 19 7 19 9
9 19 11 10 9
9 19 11 12 13
9 19 11 19 9
9 19 11 20 13
9 19 21 17 1
9 19 21 18 5
9 19 21 19 9
9 19 21 20 13
13 12 11 10 9
13 12 11 12 13
13 12 11 19 9
13 12 11 20 13
13 14 15 14 13
13 14 15 16 1
13 14 15 17 1
13 14 15 20 13
13 20 11 10 9
13 20 11 12 13
13 20 11 19 9
13 20 11 20 13
13 20 15 14 13
13 20 15 16 1
13 20 15 17 1
13 20 15 20 13
13 20 21 17 1
13 20 21 18 5
13 20 21 19 9
13 20 21 20 13
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Keith Mealy | Cincinnati, Ohio |
| 3. Brooks Garris | Dillon, South Carolina |
| 4. Rick Bessey |
John Paul II Catholic High, Tallahassee, Florida |