Thursday, September 18, 2014

254: Football Puzzle

From Sam Loyd's Puzzle Encyclopedia:
We lived way back in the country and used to order our ball by mail, according to sizes advertised in a sporting house catalog, which advised patrons to "give the exact number of inches required," and that is where the problem comes in. We were told to give the size in inches, but we did not know whether it meant the number of square inches of rubber on the surface or the number of cubic inches of wind contained within  the ball so we combined  the two principles and ordered a ball which should contain just as many cubic inches of wind as it had superficial inches of surface!

How many of our puzzlists can guess the diameter of the ball which was ordered?

Wednesday, September 17, 2014

253: Half of the blocks have paint


I liked this puzzle, so I included it.

A rectangular wooden block (not necessarily a cube) is painted on the outside and then divided into one‐unit cubes. It turns out that exactly half of the cubes have paint on them. What were the dimensions of the block before it was painted?

(many answers)

So, where do we start?
What information is really being supplied here?



source.

Tuesday, September 16, 2014

252: Circle and Quarter-circles






What do you notice about the blue figure and the yellow one?

What could we do to find perimeter?
How about area?

Monday, September 15, 2014

251: Semicircles 1


Let's talk about perimeter. What do you notice about the perimeter of the big semicircle alone and all of the smaller ones together?

What will happen if we changed this so that all the small semicircles were really, really, really small. Wouldn't that essentially be a straight line?

Sunday, September 14, 2014

250: The Shadow Knows






The man is walking down the sidewalk in the evening, at a constant speed. As he walks away from the streetlight, he casts a shadow in front of him.

If a second man were to try and keep up with the very front tip of his shadow, would he be walking at a constant speed, accelerating or decelerating, or what?

How do you know your answer is correct?

Saturday, September 13, 2014

249: Create some data

Can you create a set of data (more than 12 numbers, please) with a mean of 17 and a median of -17 and a mode of 0?

Friday, September 12, 2014

248: Raising one out of two.

Can you create a data set of more than 5 numbers so that when you add one additional number to the set, you can raise the median but not the mean?