A deterministic prediction game
“So, naturalists observe, a flea
Hath smaller fleas that on him prey;
And these have smaller still to bite ’em,
And so proceed ad infinitum.”
— Jonathan Swift, On Poetry: A Rhapsody (1733)
Swift’s fleas proceed forever. These do not: eventually there is only one flea standing. The title also gives a playful nod to Last Man Standing, the 1996 film starring Bruce Willis.
Rules: At each stage, the two closest surviving fleas meet. The smaller flea jumps onto the larger flea and absorbs it, acquiring all of its mass. The distances are then recalculated, and the process repeats until only one flea remains.
If the closest fleas are exactly the same size, the higher flea jumps. If they are also at the same height, the leftmost flea jumps.
The Demo teaches the rule. In the numbered levels, choose the flea you predict will be the last flea standing — then press JUMP and see whether you calculated the sequence.