Maths Puzzles for KS3/KS4
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The puzzled farmer

Resources

Teaching notes

Begin by asking the students which of the three items should be brought across the river first, and why. If necessary, guide the students through the solution (given in full below) and the reasoning behind each move. More able students will be able to do this unassisted.

This problem lends itself to structured questioning techniques and logical justification.

Solution

Seven crossings are needed:

  1. The farmer first takes the turkey across the river.
  2. He returns, with the boat empty.
  3. He carries the wheat across to the other bank.
  4. He takes the turkey back with him.
  5. He brings over the fox.
  6. He recrosses the river, with the boat empty.
  7. He returns with the turkey again.

This table shows which items are on each bank after each step. The farmer is always with the boat:

StepNear bankFar bank
StartBTFWR
1FWRBT
2BFWRT
3FRBTW
4BTFRW
5TRBFW
6BTRFW
7RBTFW

Key: B = Boat, T = Turkey, F = Fox, W = Wheat, R = River.

Extension

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