`2 = 1`

.```
a = b
```

we can do whatever we want to an equation as long as we do the same thing to both sides, so first add

`a`

```
a + a = b + a
```

simplify

```
2a = b + a
```

subtract

`2b`

```
2a - 2b = a + b - 2b
```

group like terms

```
2a - 2b = a + (1-2)b
```

simplify

```
2a - 2b = a + (-1)b
```

adding a negative number is the same as subtracting

```
2a - 2b = a - b
```

factor out

`(a - b)`

```
2(a - b) = 1(a - b)
```

divide by

`(a - b)`

```
\frac{2(a - b)}{a-b} = \frac{1(a - b)}{a-b}
```

re-factor to isolate the one

```
2\left(\frac{a - b}{a-b}\right) = 1\left(\frac{a - b}{a-b}\right)
```

reduce the one

```
2(1) = 1(1)
```

simplify

```
2 = 1
```

where did it go wrong? The answer will be given in a later post.

My class was given this puzzle in high school one day, and I was not the first one to see the mistake, but it was quite memorable.

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