Crusty’s Perfect Square

Aug 20, 2016

RAY: This was sent in by William Dubuvitz.

One of the mechanics in the garage has a son in high school who is very good in computer programming. He stopped by the garage one day after school and told his dad about his latest assignment.

He’s supposed to write a computer program to determine whether a large number is a perfect square. (A perfect square is a whole number or an integer that is arrived at by squaring another whole number. For example, 900 is a perfect square of 30; 196 is a perfect square of 14. 625 is the perfect square of 25. So there are no fractions, no decimals, no nothing. Just whole numbers allowed.)

Each student is assigned a different number. This kid's number is 334,912,740,121,562.

Out of the inky shadows, who appears but Crusty! And he says, "Oh, your teacher gave you an easy number."

"She did?" said the kid.

"Oh yeah. I can give you the answer right now."

What did Crusty know?


RAY: The number ends with two. And there are no perfect squares that end in two. It's impossible.

TOM: Impossible indeed.

RAY: Why? Because the units digit of any perfect square is determined by the units digit of its square root. Take the number one, for example, square it and you get one. Take the number two and square it, it comes out four. The number three comes out nine. But there is no number that you can square and get a two at the end. That's what Crusty knew. Do we have a winner?

TOM: The winner this week is R. D. Cook from Middleton, Wisconsin!

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