by John Billingham
When you were small, you probably heard the fairytale The Frog Prince. The original version of the story is rather more complicated.
The Frog Prince: original version
Once upon a time, a princess was walking through a forest and stumbled across a pond. Out of the pond rose a witch, who cackled, “Stop! I have turned a handsome prince into a frog and cast him into my pond to live with 99 other frogs. Each frog has a different number on his back. The prince has the largest number on his back, and this is your only way of spotting him. You must find him and kiss him if you want to leave my enchanted forest. The frogs will jump from the pond one by one. When each frog appears, you must decide whether to kiss him or throw him back in, never to be seen again. If you kiss a real frog, or don’t kiss any of the 100 frogs, you will never leave the forest, and the prince will remain in the pond.” And with a suitably evil laugh, the witch sank back into her murky pond. Fortunately, the princess was very good at maths, and knew the best strategy for deciding which frog to kiss.
Frog 1 hopped out of the pond with the number 2 on its back. The princess kicked it back into the pond. Frog 2 had the number 12 on its back. Better, but it received the same treatment from the princess. Frog 3 was number −6 (Did I say the numbers had to be positive?) and was duly dispatched by the princess. She repeated this for the first 37 frogs, and noted that the highest number she had seen so far was 23.2 (Did I say they had to be whole numbers?). She then waited until she saw a frog numbered higher than 23.2 and kissed it. (Of course the frog numbered 23.2 might have been the prince, and she’d then have missed him.) The frog disappeared in a puff of smoke to be replaced by a handsome prince, and they lived happily ever after (or, if you prefer unhappy endings: the witch rose from the pond laughing as the frog remained unmoved by the princess’s attentions. Oh dear! There was a higher numbered frog still to come).
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