Sometimes the truth is stranger than the fiction

A while ago, I stumbled upon this interesting math concept. The equation below proves that 2 is equal to 1; but we know for a fact that 2 does not equal to 1. So what’s wrong with this equation? Can you figure it out?

     a = x            [true for some a's and x's]
   a+a = a+x          [add a to both sides]
    2a = a+x          [a+a = 2a]
 2a-2x = a+x-2x       [subtract 2x from both sides]
2(a-x) = a+x-2x       [2a-2x = 2(a-x)]
2(a-x) = a-x          [x-2x = -x]
     2 = 1            [divide both sides by a-x]

Answers/hints will be given at the bottom of the post. But before I show you the answer, here are some more interesting brain teasers!

Land of Euclidia

The land of Euclidia has six remote towns, which we shall call A, B, C, D, E, and F. Unfortunately not all the towns are connected by telephone lines. Town A is connected to all the other 5 towns, but town B is connected to only four. Town C too, is connected to four; whereas D, E, and F are each connected to only three towns. There is a line from Town D to Town F. To what towns is Town E connected?

The Multiplication

In the following multipication problem, the letters A, B, C, and D represent four different digits. What digit should replace each letter?

 A B C D

 X     4 (X is a multiplication sign)

________

 D C B A

Height of the Tree

How tall is a tree which is 15 feet shorter than a pole that is three tiems as tall as the tree?

The Day of the Week

On what day of the week was the following statement made?

When the day before yesterday was reffered to as “the day after tomorrow,”the day that was then called “yesterday” was as far away from today as today is from next saturday.

The answers…

Highlight below.

For 2=1 -> You cannot divide by zero (2nd to last step)
Land of Euclidia -> Town A, B, and C
The multipication -> A=2 B=1 C=7 D=8
height of the tree -> 7.5 Feet
The day of the week-> Monday

Sources

2=1, and Creative Publications: Test of Genius

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