After many adventures in Wonderland, Alice has once again found herself in the court of the temperamental Queen of Hearts. She’s about to pass through the garden undetected when she overhears the king and queen arguing that 64 is the same as 65.
When Alice challenges the queen, four cards arrive. Two trapezoid cards have non-diagonal sides measuring 5x5x3. Two long triangle cards with non-diagonal sides measure 8×3. All four lay down on a chessboard measuring 8×8.
Then the cards rearrange themselves on a board measuring 5×13. They appear to take up the same space, confounding Alice. Could 64 be the same as 65?
As Lewis Carroll said, “one can’t believe impossible things.” Learn how to solve the Alice in Wonderland riddle, otherwise known as the Mathematical Chessboard Paradox. This TED-Ed puzzle by Alex Gendler explores rise over run, the Fibonacci sequence, and the golden ratio. Direction by Artrake Studio.
Then read more about Oxford-based mathematical lecturer Charles L. Dodgson, aka Alice author Lewis Carroll, in Nature: Logic and Lewis Carroll.
Carroll believed that beyond their entertainment value, mental recreations such as games and logic puzzles conferred a sense of power on the solver. This, he felt, enabled them to analyse any subject clearly and, most important, to detect and unravel fallacies.
Also related: Read Alice in Wonderland online for free.
Then watch more TED-Ed puzzles on TKSST.
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