“A few years ago, the king decided your life would be forfeit unless you tripled the gold coins in his treasury. Fortunately, a strange little man appeared and magically performed the feat. Unfortunately, you promised him your first-born child in exchange for his help — and today he’s come to collect. Can you figure out how to outsmart the man and keep your baby?”
This twist on the tale of Rumpelstiltskin reveals a function-focused logic lesson by mathematician and Math for Love co-founder Dan Finkel: The Infinite Gold Riddle. Here’s how it works, according to the strange little man:
“‘My bag,’ he explains, ‘increases the number of gold coins placed inside it in a very special way. If I take any number of coins and place them in, more will come out. And if I place those in the bag again, the total that comes out will be three times whatever I began with.'”
“He takes 13 coins and places them in the bag, then removes the contents. ‘I’ve used the magic once, not twice,’ he says. “Tell me how many coins are in my hand and I’ll have mercy.'”
How many coins is he holding? The key to this logic puzzle is mostly in using the numbers you know to determine the numbers you don’t know.
Remember: “If you use the magic twice, the initial number of coins will always be tripled.” Pause at 1m53s to solve the challenge without help. Here are the rules:
Plus, from TED-Ed’s Dig Deeper for this lesson:
“There are many ways to generalize this situation. Here are a few:
-What would the magic do to 17 coins? To 23? To 30?
-Is it possible to end up with any number of coins after applying the magic once? For example, if I want the bag to hold exactly 47 coins, is there a number I can put in first that will end up with 47 coming out?
-Can you write a formula or description for how the magic behaves?
-What if the bag quadrupled the coins when you applied it three times. Could you find what would happen to 13 coins in this case? Does this situation generalize?”
Semi-related reading: Banach-Tarski and the Paradox of Infinite Cloning.
Watch these related videos next on TKSST:
• Can you solve the counterfeit coin riddle?
• Can you solve the dark coin riddle?
• Can you solve the penniless pilgrim riddle?
• The Story Of King Midas, a stop-motion classic by Ray Harryhausen (1953)
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