The puzzle of Mirror Images

I ran into the puzzle of why images in the mirror are reversed left-right but not up-down. Then I found this blog, which seems to have been discontinued since 2003.

The host appears to be a grade school science teacher and was gathering puzzles and researching for the answers for his students.

So about mirror images, mirrors do not actually reverse image sideways. It is our perception of left and right that leads us ask the wrong question. He describes a simple solution:

Stand in front of a mirror facing north yourself. Raise your right arm to point east, your mirror image is also pointing east. Raise your left arm to point west, and your mirror image is pointing west. The same thing happens when you point up or down. But if you point your finger to the north (into the mirror), your image will points out of the mirror and to the south!

So the fact is, mirrors only reverse the direction of the object by the axis perpendicular to the mirror surface, just as the physical law depicts what happens to light when it hits a mirror - light traveling into a mirror travels backward (got reflected).

The host also suggests a few websites and books to read. This The Annotated Alice: The Definitive Edition seems very interesting. The books includes the original stories of Alice in Wonderland and Through the Looking Glass by Lowell Carroll and original illustrations, and very detail annotations by Martin Gardner on the historical context of the jokes and logical, topological and mathematical paradox.

Kill now, report later - answer

The answer to yesterday's puzzle - why the couple is not accused for reporting the dead body two weeks after they left the scene:

Two weeks after they left the island, they see the dead body in the photos they take outside the cottage.

My phone number

AEB-FDJ-EIAF

Each of the letters from A to J represents a number between 0 to 9. Deduce the number each of them represent from the following equations. When two letter are written next to each other without an operator, the left letter represents the decimal digit of a two-digit number.

D+D+D = F
H+H = B
G+B+E = F+A+C
I+A = CC
F*D = JG
B/H = J
D*H = CJ
A*H = JE
I/D = J
d/I = H/B

Kill now, report later

An couple spent a week in Honolulu for their 20th anniversary. They rented a cottage and roamed the island and enjoyed the beach. Two weeks after they came home, they called the police in Honolulu and told them that they had found a dead body in the bush behind the cottage they stayed. The police went there and found the corpse. However, the couple was not accused of reporting two weeks after they left. Why?

Brainteasers that I managed to solve - 2

I got this wrong the first time but I figured out how to solve it given the correct answer:

There are 8 billiard balls of the same size. One of them is slightly heavier than the rest. You are given a classical two-pan balance. What is the minimum number of time you need to put the balls onto the balance to tell which ball is heavier.


The answer is:

Two
Take any 6 of the 8 balls and split them into two groups of 3. Place each group of the balls onto each side of the balance. If they weigh the same, the heavier ball is one of the two left behind. If one of the groups is heavier, put any two of the 3 onto each side of the balance. It will tell you either one of the two is heavier, or if they weigh the same, the one left behind is the heavier one.

Brainteasers that I managed to solve - 1

You are given two buckets, one can hold 5 pints and the other hold 3. Now you are asked to take exactly 7 pints of water from a river with these buckets in one single trip. How can you do that?


The answer is:

Fill the 5-pint bucket with water, and use the water to fill the 3-pint bucket. Now you have 2 pints of water left in the 5-pint bucket. Then you empty the 3-pint bucket and pour in the 2 pints of water. Now you have an empty 5-pint bucket and a 3-pint bucket with 2 pints of water. You know what to do next.