Mathematical Riddles

Homeless man and cigarette butts

A homeless man is able to create a cigarette from 3 cigarette butts. Cunning as a fox, he manages to find 28 cigarette butts.

How many cigarettes will he get to smoke ?

The age of the two children

Emily and William are brothers and sisters. One day, the two children have a discussion in their rooms:

- You know Emily, if I took 2 years at my age and I gave them to you, you would double my age.
- Yes, but if you gave me 3 years of your age, it would make mine three times greater than yours.

How old are the two children?

The heaviest of the little bags of gold

We have 9 small bags of gold and a balance with 2 trays perfectly balanced. One of the small bags of gold is heavier than the others.

How can one identify with certainty what is this bag, in only 2 weighings?

The age of the three girls

- The multiplication of their 3 ages gives the number 36, replies the other.
- I can not find their ages, responds first.
- The addition of their ages gives the same number as that which is inscribed above this porch, just in front of us.
- I still can not answer, said the first.
- The eldest is blonde.
- Oh yes, of course, I know their respective ages, now!

What are the respective ages of the three girls?