Saturday, April 25, 2015

444: Floorlamp

The floor lamp casts a shadow.
Straight line AB is drawn on a wide, spacious floor. A lamp is at a height of 8  m above point C, which is located on line AB.  Line CD is perpendicular to line AB.  A rectangular solid 5 m by 3 m by 4 m is on the floor as shown.  The box is 2  m from line AB and a meters from line CD. Assume the lamp is a point source and will cast a perfect shadow. Given that the rectangular solid casts a shadow with area 90  m², determine the distance a (in meters).

  • Does the 2m distance from the wall matter to the shape of the shadow?
  • How does the distance a change the area of the shadow?
  • What shape is that shadow on the floor? 
  • Are the edges of the shadow guaranteed to parallel with the edges of the box?
  • How far away is that box from the light? 
It's another Five Triangles puzzle

Thursday, April 23, 2015

442: Square Root

x² = 81 has two solutions, -9 and 9.

But does √81 have one solution or two? Is it correct to say that √81 = +9 and -9?

Or should we be saying that √81is an expression and that 9, 18/2, 27^(2/3), and 1+6+2, are equivalent expressions?

Wednesday, April 22, 2015

441: How many K?

Edited out the answer and some hashtags  ...

For how many integers k is 10,000 - k² positive?

Tuesday, April 21, 2015

440: Revenge of the Mad Hatter

There are three red hats and two black hats on a hatstand.

Melba, Fran, and Brent line up in a single file line, and the mad Hatter places a hat on each person’s head and tosses the rest into a box where no one can see them.

The Mad Hatter takes off Brent's blindfold. Brent, who could see Fran’s hat and Melba’s hat, says, “I don’t know what color my hat is.”

The Mad Hatter takes of Fran's blindfold. Fran, who could only see Melba’s hat, says, “I heard what Brent said, but I don’t know what color my hat is.”

As the Mad Hatter moved to take off Melba's hat, she said, “I don't need you to take off my blindfold. I know what color my hat is.”

What color is Melba’s hat and how does she know?

Monday, April 20, 2015

439: Fraction / Decimal Tic-Tac-Toe

We all know that playing the middle of a tic-tac-toe game ensures that you can never lose if you play it right, but this one seems to be a bit trickier.

Where is the best place to start?

Sunday, April 19, 2015

438: NY Daily Statistics

NY Daily News had this:
Government-hating gun owners are shooting themselves in the foot.

The gun-buying frenzy triggered by the 2012 Sandy Hook school shooting pumped $875 million into federal coffers in 2013 alone, according to That’s because the Treasury’s Alcohol and Tobacco Tax and Trade Bureau collects a 10% tax on ammo sales and a nearly 10% tax on gun sales. The tax revenue on guns and ammo reached an all-time high the year after the Sandy Hook Elementary School massacre, which left 27 students and teachers dead and triggered fears of stricter gun laws.

The roughly $255 million in tax revenue on ammunition alone brought in by the feds in 2013 was nearly double the 1991 tax receipts for handguns, long guns and ammo combined, according to Vocativ.

Is that graph properly done?
Is it misleading?
Is the data itself misleading?