Three guards, three prisoners, one two-seat boat

Question

Three guards and three prisoners must cross a river. The boat holds at most two people, and someone must row it each way; both guards and prisoners can row. If, on either bank (or in the boat), the prisoners ever outnumber the guards present, the prisoners overpower them. A bank with prisoners and no guards is fine. What is the fewest number of one-way crossings needed to get everyone across safely? Give the sequence. (This is the old missionaries-and-cannibals puzzle in a different costume.)

Accepted Answer

Eleven crossings. Write G for guard and P for prisoner, and track who is on the far bank. 1. Two prisoners cross. Far bank: P P. 2. One prisoner returns. Far: P. 3. Two prisoners cross. Far: P P P. Near bank: G G G. 4. One prisoner returns. Far: P P. Near: G G G P. 5. Two guards cross. Far: G G P P. Near: G P. (Equal numbers on both banks: safe.) 6. One guard and one prisoner return. Far: G P. Near: G G P P. 7. Two guards cross. Far: G G G P. Near: P P. 8. One prisoner returns. Far: G G G. Near: P P P. 9. Two prisoners cross. Far: G G G P P. Near: P. 10. One prisoner returns. Far: G G G P. Ne…

Three guards, three prisoners, one two-seat boat

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