Knight Swap Puzzles: Solutions
How to solve knight swap puzzles: the ring trick behind Guarini’s puzzle of 1512, and the fewest moves for every board, from one knight each to eight.
In a knight swap puzzle, white and black knights stand on a small board and must change places. Knights move as in chess, two squares one way and one square the other, but here they never take each other: they only move onto empty squares. Knight Swap has seven boards. This guide shows the trick that makes them easy to see and gives the fewest moves for every one.
How the game works
Tap a knight and then one of the lit squares it can reach. Every white knight has to end on a square where a black knight started, and every black knight where a white one started. A small dot on each square shows which colour finishes there. The fewest moves earn three stars.
Squares are named as on a chessboard: columns a, b, c and so on from the left, rows 1, 2, 3 from the bottom. So on a 3 × 3 board, a3 is the top left corner.
The ring trick
The puzzles look hard because knights jump over each other’s heads. The trick, made famous by the puzzle writer Henry Dudeney, is to stop looking at the board. Put a button on each square and tie a string between every two squares a knight’s move apart. Then pull the strings out straight. On a 3 × 3 board the eight outer squares untangle into a single ring, and the centre has no strings at all: no knight can ever reach it.
On a ring, the knights simply walk round. Nobody can overtake anybody, so every knight must travel the same way round, and the question becomes how far.
One Each
One white knight on a3 and one black knight on c1. Eight moves:
- White a3 to c2. 2. White c2 to a1. 3. White a1 to b3. 4. Black c1 to a2. 5. White b3 to c1. 6. Black a2 to c3. 7. Black c3 to b1. 8. Black b1 to a3.
Four Corners
White knights on a4 and d4, black knights on a1 and d1. Eight moves, each knight moving twice:
- White a4 to b2. 2. White d4 to c2. 3. Black d1 to c3. 4. White b2 to d1. 5. Black a1 to b3. 6. White c2 to a1. 7. Black b3 to d4. 8. Black c3 to a4.
Guarini’s Puzzle
White knights on a3 and c3, black knights on a1 and c1. On the ring the colours alternate in pairs, and each knight has to go four steps round: 16 moves.
- White a3 to c2. 2. White c3 to b1. 3. Black a1 to b3. 4. White c2 to a1. 5. White b1 to a3. 6. White a3 to c2. 7. Black c1 to a2. 8. Black b3 to c1. 9. Black a2 to c3. 10. Black c3 to b1. 11. White a1 to b3. 12. White c2 to a1. 13. Black c1 to a2. 14. White b3 to c1. 15. Black a2 to c3. 16. Black b1 to a3.
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The Broken Board
A 4 × 4 board with the corners a1 and d4 missing; white knights on a4 and b3, black knights on c2 and d1. Twelve moves:
- White a4 to b2. 2. White b3 to d2. 3. Black c2 to a3. 4. White d2 to b1. 5. Black d1 to c3. 6. White b2 to d1. 7. Black a3 to c4. 8. Black c4 to d2. 9. White b1 to a3. 10. White a3 to c2. 11. Black d2 to b3. 12. Black c3 to a4.
Three a Side
Three white knights down the a file and three black knights down the d file of a 3 × 4 board. Sixteen moves:
- Black d3 to c1. 2. White a1 to b3. 3. Black d1 to c3. 4. Black c3 to b1. 5. White a2 to c3. 6. White c3 to d1. 7. Black c1 to a2. 8. White b3 to c1. 9. Black b1 to c3. 10. White a3 to b1. 11. Black d2 to b3. 12. White b1 to d2. 13. Black c3 to b1. 14. Black b3 to a1. 15. White c1 to d3. 16. Black b1 to a3.
Two Rows of Five
Five white knights on row 3 of a 3 × 5 board and five black knights on row 1. Fourteen moves:
- White e3 to c2. 2. Black c1 to e2. 3. White d3 to c1. 4. Black d1 to e3. 5. White c3 to d1. 6. Black e1 to d3. 7. White c2 to e1. 8. Black b1 to d2. 9. White a3 to b1. 10. Black a1 to c2. 11. White b3 to a1. 12. Black e2 to c3. 13. Black d2 to b3. 14. Black c2 to a3.
The Long Board
Four white knights on a3, b3, a1 and b1, four black knights on d3, e3, d1 and e1. With only seven empty squares it takes 22 moves:
- Black d3 to c1. 2. Black e3 to c2. 3. Black c1 to e2. 4. White b3 to c1. 5. White a1 to b3. 6. Black c2 to a1. 7. White a3 to c2. 8. White c2 to e3. 9. White c1 to d3. 10. Black e1 to c2. 11. White d3 to e1. 12. Black d1 to c3. 13. Black c3 to a2. 14. White b1 to c3. 15. White c3 to d1. 16. White b3 to c1. 17. White c1 to d3. 18. Black a2 to c1. 19. Black e2 to c3. 20. Black c3 to b1. 21. Black c1 to b3. 22. Black c2 to a3.
Where the puzzle comes from
Paolo Guarini di Forli posed the four knight puzzle in 1512, which makes it one of the oldest chess puzzles on record. Dudeney’s button and string method, published in the early twentieth century, turned it from a head-scratcher into something you can see at a glance.
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Questions and answers
How many moves does Guarini’s puzzle take?
Sixteen. The eight outer squares of the 3 × 3 board form one loop of knight moves, and each of the four knights goes four steps round it.
Can a knight reach the centre of a 3 × 3 board?
No. From the centre every knight move would leave the board, so the centre square plays no part in Guarini’s puzzle.
What is the button and string method?
Mark each square with a button and tie a string between squares a knight’s move apart, then pull the strings straight. The knights’ paths become simple loops and lines.
Written by the DailyGameClub team from the rules as DailyGameClub plays them. Updated October 27, 2026. New to a word? See the glossary. Spotted a mistake? Tell us.