Brain Teasers: Equation Gone Wrong

Hey all! Can anyone figure out what went wrong?

a = b

ab = b^2

ab - a^2 = b^2 - a^2

a(b - a) = (b - a)(b + a)

a = b + a

                                                          a = b;          a = a + a

a = 2a

1 = 2?

What happened?

Solution: Look at Steps 4 and 5 in my justification above:

a(b - a) = (b - a)(b + a)

a = b + a

If a = b, then b - a = 0, so the real justification would be:

a(0) = (0)(b + a)

0 = 0

This means I divided by 0 in my justification, which is impossible according to the laws of mathematics.

Hope you enjoyed!

Fast Facts

Hey! Here are some fun math tips.


Fact 1:

1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25

See? The sum of odd consecutive numbers starting from 0, will always be a perfect square number no matter how far you go. Check it out!

Fact 2:


4% of 100 = 100 % of 4
6% of 38 = 38% of 6
5% of 10 = 10% of 5
7% of 50 = 50% of 7

Catch the drift?

Fact 3:

(a * b) * (c * d) = 100(ac) + 10(ad + bc) + (bd)

This is just the Rainbow Method simplified into an equation!

Fact 4: 

To square 2 digit numbers ending with ‘5’ (Example: 75 × 75)
1.  Take the first digit ‘7’ multiply by the number after ‘7’ => 7 × 8 = 56 

Now add 25 after the number. 56(25) = 5625

Hope you all enjoyed!