Posts Tagged ‘quadratic residues’

Balls Under Cups

Wednesday, May 22nd, 2019

One sunny Saturday afternoon while Lennie was taking his daily stroll in the city, he passed a young woman walking bent over, hands on her face, crying.

“What’s the matter, girl,” said Lennie, stepping alongside.

“I’ve just been cheated of 20 quid I had saved up to buy my sick mother some medical supplies she needs, hoping to win more,” she sobbed.

She explained that a man sitting at a makeshift table on the bridge by the river had cheated her using cups and a ball.

“Come with me,” said Lenny, taking her resolutely by the hand, “let’s see about this.”

“So you wanna play, matey,” said the trickster to Lenny, spitting tobacco and deftly moving the cups and ball about on a small table supported by two plastic beer cases.

“Sure, pal,” said Lenny, “looks easy enough to spot which cup is hiding the ball. You’re going to lose.”

The game proceeded to its inevitable conclusion.

“You’re really good at this, pal. Looks like I owe you 50 quid,” said Lenny, looking impressed.

“Right you are, matey. Pay up.”

“Certainly, here you have the cash,” said Lenny, placing a fifty quid note on the table. “But I have a proposition for you, if you are a daring gambling man.”

“Eh, what’s dat,” said the trickster with a sly grin.

“Well, if you win, I’ll pay you 200 quid, if you lose you pay me 100 quid. You need to solve a small problem in division,” said Lenny.

“And what kind of trick is that?”

“Simple, really. I’ll give you five attempts to find a square number which divided by five gives a remainder of two or three.” said Lenny.

“Uhh… Give me an example,” said the trickster.

“Well, take any number such as six and square it, in this case getting 36, which divided by five gives a remainder of one. You just need to find a number that gives two or three as a remainder. Easy peasy,” said Lenny.

“Matey, you just lost another 200 quid. I’ve got a quick mind for figures, see,” said the trickster, tapping his temple and chewing more rapidly on his tobacco.

“Okay, pal, let’s put our money on the table,” said Lenny.

After trying five times, the trickster was unable to find such a number and, swearing to high heaven, had to concede a loss.

Lenny, who was much bigger than the trickster, picked up his newly won 100 quid plus his stake of 200 and walked away with the girl.

“Next time stay away from such people,” said Lenny handing her the 20 quid she had lost, plus a fiver. She gave him a big hug followed by a quick kiss, and ran off.

Can you find such a number?


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