## Wednesday, October 28, 2015

### Sam Loyd's 14-15 Puzzle - Part II

10/28/2015

Now for the truth.

Sam did not invent the 15 puzzle.  Sam did not have anything to do with the 15 puzzle craze that started late in 1879.  And he did not start the craze about solving the puzzle with the 14 and 15 reversed.

The puzzle you saw yesterday came out in 1914, 3 years after Sam Loyd died.  His son published a lot of the material that Sam had left in his papers, so I don't know for sure how much of what is said about the puzzle is true - though I do know quite a bit of it is false.

The \$1,000 prize was never claimed, because it is impossible to solve with the 14 and 15 reversed (or any two numbers for that matter).  So it was a safe bet.  On that Sam knew he would never have to pay out.

However, it is an interesting puzzle.  And it is worth studying.

OLD AND NEW PROBLEMS: Sam suggests there is a trick that will allow the original problem (with the 14 and 15 reversed) to be solved.  He also suggest three new problems developed from the original puzzle which are worth sharing:
The Original Problem: Sam seems to hint that there is a trick that will allow the original problem to be solved.  “The real trick of the puzzle could only be performed by changing the 9 into a 6, and the 6 into a 9, by turning them upside down during the manipulation of the blocks.”

 1 2 3 4 1 2 3 4 5 9 7 8 -> 5 6 7 8 6 10 11 12 9 10 11 12 13 15 14 13 14 15
Figure 1:
Second Problem: Start again with the blocks as in figure 1 and move them so as to get the numbers in regular order, but with the vacant square at the upper left hand corner instead of lower right-hand corner; see figure 2.
 1 2 3 4 1 2 3 5 6 7 8 -> 4 5 6 7 9 10 11 12 8 9 10 11 13 15 14 12 13 14 15
Figure 2:
Third Problem: Start with figure 1, turn the box a quarter way round and so move the blocks that they will rest as in figure 3.
 13 9 5 1 -> 1 2 3 4 15 10 6 2 5 6 7 8 14 11 7 3 9 10 11 12 12 8 4 13 14 15
Figure 3
Fourth Problem: This is to move the pieces about until they form a “magic square,” so that the numbers will add up thirty in 10 different directions (4 rows, 4 columns and the 2 main diagonals - but he does not say what the magic square look like or where the blank space goes).  See Figure 4.
 1 2 3 4 13 1 6 10 5 6 7 8 -> 14 2 5 9 9 10 11 12 12 11 7 13 15 14 3 15 8 4
Figure 4:
Tomorrow we will see if any of these problems can be solved or if Sam is hoaxing us one more time.

David

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