Simpler Math Puzzles

  1. A chicken and a half can lay an egg and a half in a day and a half. How long does it take twelve chickens to lay twelve eggs?

  2. You have two quarters of equal size. One is held still in the centre. The other is put so it touch the central quarter at one point and the head is facing to the left. It is turned around the first quarter so that its side is always in contact. After travelling the circumference of the quarter, the head is again facing to the left. How many rotations does the outside quarter make?

  3. A cube is suspended from a string and lowered into a beaker of acid. Half of the volume of the cube is eated away. What shape do you see on the bottom of the cube?

  1. A day and a half. (strictly mathematically speaking, since your question is based on half eggs laid by half chickens, which are unlikely to be found on any real world poultry farm.)

  2. Twice.

  3. Poorly worded question. First, do you lower the cube into the acid until it is halfway submerged and wait for the acid to dissolve the lower half, or do you submerge the cube completely and remove it as soon as half the mass has dissolved? Secondly, at what point is the string attached to the cube. It could be at a corner, along an edge, or at any point on one of the faces. Third, you ask “What shape do you see on the bottom of the cube?” Depending on how it was submerged, the remaining object won’t be a cube anymore.

Making a few assumptions: If the string is attached at one corner of the cube, and the cube is lowered halfway into the acid, the shape of the resulting cross section will be a hexagon.

Yes, yes and yes; it was a poorly worded question, since I meant the string to be attached to a corner :o

Very good.

Simple for Cecil, but not that other “smart” columnist:

Depends on the point of view. From the point of view of the inside quarter, 1. From the point of view of an outsider, 2.

Same thing with the Earth and the moon. How many roations does the moon make per cycle? From the Earth, none, we always see the same side. From another planet, 1, because they could see all sides of the moon.