Run Detail

Classic solution (farmer can only take one item at a time)

• Start: Left bank has Farmer, Fox, Chicken, Grain. Right bank is empty.

1. Farmer takes Chicken to the right bank.

   • Reason: If we leave Fox and Chicken together on the left bank, the Fox would eat the Chicken. On the right bank, Chicken is safe with the farmer.

2. Farmer returns alone to the left bank.

   • Reason: Now the left bank has Fox and Grain (safe together without the farmer). The Chicken is on the right bank with the farmer, also safe.

3. Farmer takes Fox to the right bank.

   • Reason: We need to move the Fox across. The left bank now has Grain alone (safe). On the right bank, Chicken is present but the farmer is there, so it’s safe for the moment.

4. Farmer brings Chicken back to the left bank.

   • Reason: If we left Chicken on the right bank with Fox when we later move Grain, the Fox would eat the Chicken. By taking Chicken back, the right bank ends up with only Fox (safe unsupervised), and the left bank has Grain and Chicken with the farmer.

5. Farmer takes Grain to the right bank.

   • Reason: Now the right bank has Fox and Grain with the farmer; the left bank has Chicken alone (safe).

6. Farmer returns alone to the left bank.

   • Reason: The right bank has Fox and Grain unsupervised, which is safe since Fox does not eat Grain.

7. Farmer takes Chicken to the right bank.

   • Result: All four are safely on the right bank: Farmer, Fox, Chicken, Grain.

Summary of reasoning:

• Do not leave Fox alone with Chicken.
• Do not leave Chicken alone with Grain.
• The farmer must shuttle an item across (and sometimes bring one back) to ensure both banks never have an unsafe pairing without supervision. This sequence achieves that and gets everyone across safely.