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New Scientist Enigma 581 – Trail Blazing Cards

by Brian Gladman on October 26, 2020

by Keith Austin

From Issue #1734, 15th September 1990

We spent the day camped at the entrance to Apache Pass waiting for the cover of darkness. I passed the time playing cards with a grizzly old prospector, using a pack given him by Billy the Kid.

He took the spades from ace to ten and laid them in a row so:

6 2 9 7 3 10 8 1 4 5

where 1 is the ace.

“That’s the order Wyatt Earp dealt me just before the gunfight at the OK Corral. You can exchange any to cards provided the numbers on them are consecutive but the cards are not next to each other. For example, you can exchange the 7 and the 8, or the 2 and the 3, but not the 4 and the 5”.

“So I can exchange the 7 and 8 and get:

6 2 9 8 3 10 7 1 4 5

and then exchange the 3 and 4 and get:

6 2 9 8 4 10 7 1 3 5

and then exchange the 4 and 5 and get:

6 2 9 8 5 10 7 1 3 4

and so on?” I asked.

“You’ve got it. Now look at this old treasure map I got from Geronimo. It has 6 rows of numbers on it:

A: 7 2 10 9 4 5 3 1 8 6
B: 5 9 2 4 8 1 3 10 7 6
C: 7 4 5 2 1 10 8 3 6 9
D: 4 5 7 8 1 3 2 10 6 9
E: 10 3 4 2 1 9 6 5 7 8
F: 6 10 8 5 3 1 2 4 7 9

“Geronimo said the to discover the treasure it was necessary to find which of these six rows can be obtained from Wyatt’s row by the allowed
operations.”

Find all those of the six rows which can be obtained from Wyatt’s row.

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