Maths Problem

kingfisher 11 · active quizzer Joined: 12 Nov 2007 Posts: 91

Not looking for and answer particularly but does anyone think there is not a unique answer to this.

"A teacher has some cards numbered from 1 to "n". One fifth of the cards have square numbers on them. How many cards did the teacher have?"

wildrover · Posted: Thu Feb 12, 2009 10:49 pm Post subject:

He has 25 cards and it's certainly the only answer.

silverside · pro quizzer Joined: 10 Jun 2007 Posts: 229

The answer is 25 cards

In the sequence 1 to 25 there would be 5 square numbers which is a fifth of 25

1x1=1
2x2=4
3x3=9
4x4=16
5x5=25

pulse876 · pro quizzer Joined: 03 Jan 2009 Posts: 130 Location: Bath

So why can't he have 15 cards (which contain the 3 square numbers of 1, 4 and 9) or 20 cards (which contain the 4 square numbers of 1, 4, 9 and 16)?

wildrover · Posted: Fri Feb 13, 2009 10:10 am Post subject:

You got me - those look like valid answers to me.

pulse876 · pro quizzer Joined: 03 Jan 2009 Posts: 130 Location: Bath

I guess people will be drawn to 25 as the answer because they are thinking about square numbers to solve it. But the question does not specify that n has to be a square number so I can't see anything wrong with 15 or 20 as alternative answers.

Similarly in the same quiz there is a question about a line through points A and B and you have to give the coordinates of a point P on that line that is twice as far from A as from B. The obvious answer is that P lies on the line between A and B. But the question doesn't specify that P has to be between A and B so an equally valid answer is for P to be on the extended line to the right of point B.

Not the cleverest pair of questions I've ever seen!

kingfisher 11 · active quizzer Joined: 12 Nov 2007 Posts: 91

Thankyou everyone for your respone

HighVoltageNights · newbie quizzer Joined: 06 Apr 2009 Posts: 1

Surely the teacher has 'n' cards

silverside · pro quizzer Joined: 10 Jun 2007 Posts: 229

Yeah but, no but, yeah but, no but....mmmmm