# 2=1? - math puzzle

Suppose: a = b

It then follows that

a * a = a * b

a^2 = a * b

a^2 - b^2 = a * b - b^2

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

a + b = b

a + a = a

2 * a = 1 * a

2 = 1

Is this derivation really correct? Or is there somewhere a mistake? If so, where?

It then follows that

a * a = a * b

a^2 = a * b

a^2 - b^2 = a * b - b^2

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

a + b = b

a + a = a

2 * a = 1 * a

2 = 1

Is this derivation really correct? Or is there somewhere a mistake? If so, where?

# Sundays child - math puzzle

Recently, somebody told: "My grandfather was born on the first sunday of the year. His seventh birthday was also on a sunday!" In which year was this grandfather born?

# Number exchange - math puzzle

A number has 6 different digits. If the last digit is moved to the front, then a new number is formed which is exaclty 5 times the old number. With which number did we start?