October 2004


In this edition we have two brainteasers

Brainteaser #1 - Get out of Jail

The prisoner sat alone in his cell staring through the bars at the six doors to the guardroom beyond them. Suddenly, there was the sound of footsteps. One guard came in through door A and a second entered through door F. They unlocked the cell door. "We shall set you free," said one of the guards, "but first you must pass through all six doors, each door once only. Three are entrances only and three are exits only. Door A must be followed by door B or E; B by C or E; C by D or F; D by A or F; E by B or D; and F by C or D." With that the guards left through door B. In what order must the prisoner pass through the doors? ...

This brainteaser has two aspects:

  1. First, solving the correct order of the doors.
  2. Second, noticing your thinking strategy for solving the problem and finding an alternate thinking strategy.

Thanks to the folks at www.grand-illusions.com for cataloging this brainteaser.



OK - Here is the answer

The order is C F D A B E


A Verbal Thinking Strategy (provided by barryispuzzled.com)

The guards entered through doors A and F and exited at door B. The prisoner must alternate exits and entrances. Let the unknown entrance be X. With a "_" denoting an exit door the possible orders are:

(A) _A_F_X ; (b) _F_A_X ; (c) _X_A_F ; (d) _X_F_A ; (e) _A_X_F ; (f) _F_X_A

Neither (a) nor (c) are possible since A is followed by B or E and neither leads to F. Since A can only be preceded by D, (e) and (f) are possible as DA_X_F and _F_XDA, respectively. With D used, door F can only be preceded by C to give DA_XCF and CF_XDA, respectively. Door B must occupy the remaining space in each possibility (third door is exit) so X=E but C cannot follow E in the former and for the latter, B cannot follow F.

This eliminates (e) and (f). Since only D precedes A, (b) is possible as _FDA_X and (d) as _X_FDA. For (d), the exit B must occupy a "_" but cannot be followed by F, and if it is the first door, neither the C or E that must follow as X can be followed by the remaining E or C, respectively.

This only leaves (b) and only C (of the possible B,C,E) can precede F as CFDA_X and B must occupy the final "_" as an exit leaving E=X. Notice that the condition that E is followed by B or D cannot be satisfied until the prisoner has completed his task and finally wins his freedom through B or D!

A Visual Thinking Strategy (provided by Innovate)


Another exercise to strengthen Visual Thinking.

Brainteaser #2 - Escape! by D. S. Cornwell




Want a hint

First, there really is a solution . We found early positioning one small square into upper right is important.



A Solution

Our solution has two small squares positioned into the upper right horizontal.

Some ways of thinking are more powerful than others. We found thinking in terms of moves continually led us to dead ends. We found thinking in terms of positioning was very promising. We have been able to get it down to 36 moves. We are looking for the line of thinking that will get it to 27 moves.

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