Sam Loyd's Son's Dissection:
What Is Wrong?

The pieces of the 8×8 square dissection that combine into a 5×13 rectangle can also be arranged into a shape comprising 63 small squares. To see how this works drag the colored pieces from one rectangle into their designated locations in the other.)

(In the applet you can either drag the pieces manually or make them move automatically by pressing the "Animate" button.)

Martin Gardner attributes this puzzle to Sam Loyd's son who adopted his father's name and occupation. Greg Frederickson attributes the puzzle to Walter Dexter (1901), which is likely to be an earlier source.

This rearrangement is more sensitive to small size discrepancies involved in the dissection. The overlaps are more prominent even where I tried to programmatically conceal them (Check the "Cheat" button.)

References

1. G. N. Frederickson, Dissections: Plane & Fancy, Cambridge University Press, 1997, 273-274
2. M. Gardner, Mathematics Magic and Mystery, Dover, 1956, pp. 133-134

Dissection Paradoxes

• Curry's Paradox
• Dissection of a 10×13 Rectangle into Two Chessboards
• A Faulty Dissection
• Hooper's Paradox
• John Sharp's Paradox
• Langman's Paradox
• Popping A Square
• Sam Loyd's Son's Dissection

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