# Riddles with numbers Do you like riddles with numbers? Here we have some number brain teasers you can try to solve. Can you solve these? These are hard number riddles with answers, but do not look at the answer until you have tried to solve them.

## The hourglass

For a perfect breakfast, you want to boil an egg exactly 15 minutes. You hve two hourglasses – one for 7 minutes, another for 11.
How can you tell when the eggs are done?

Turn both hourglasses when you start boiling the egg.
After 7 minutes, the 7 minute hourglass will run out. Turn it over to restart it.

In another 4 minutes, the 11 minute hourglass will run out.

At this point, turn the 7 minutes hourglass. It will now take 4 minutes to empty.

When it does, your egg will have cooked for exactly 15 minutes (7 minutes + 4 minutes + 4 minutes).

## Crossing the bridge

It is late at night and dark. A group of 4 friends, with just a flashlight, come to a river.
There is a narrow bridge, but it can only hold two people at a time.
They have one torch and, because it’s night, the torch has to be used when crossing the bridge.
Ann can cross the bridge in 1 minute, Bert in 2 minutes, Caroline in 5 minutes, and David in 8 minutes.
When two people cross the bridge together, they must move at the slower person’s pace.
They have a bus to catch so they have to get over the bridge in a maximum of 15 minutes.
How can they achieve this?

Ann and Bert cross the bridge together. This takes 2 minutes.
Ann then returns with the torch that takes 1 minute.

Caroline and David then cross the bridge together which takes 8 minutes.

Bert then comes back with the torch. This takes another 2 minutes.

Finally Ann and Bert cross the bridge again, taking another 2 minutes for a total of 15 minutes.

## Age of the children

An insurance salesman walk up to a house and knocks on the door.
A woman answers, and he asks her how many children she has and how old they are.
She says I will give you a hint. If you multiply the 3 children’s ages, you get 36.

He says this is not enough information. So she gives a him second hint.

If you add up the children’s ages, the sum is the number on the house next door.

He goes next door and looks at the house number and says this is still not enough information.
So she says she’ll give him one last hint which is that her oldest of the 3 plays piano.

How old were the children?

If we start from the top and go down, we get the following:

1) She says, «If you multiply my 3 kids’ ages, you get 36».
We know that she has 3 children and if you multiply the age dems with each other you get 36.
We then find which three numbers multiplied by each other become 36. We then get the following:
1 x 1 x 36 = 36
1 x 2 x 18 = 36
1 x 3 x 12 = 36
1 x 4 x 9 = 36
6 x 6 x 1 = 36
2 x 2 x 9 = 36
2 x 3 x 6 = 36
3 x 3 x 4 = 36

He says there is not enough information. Understandably, there are 8 combinations that can provide the answer.

2) We now get hint number 2: «If you sum the children’s age, the sum is equal to the house number of the house next door».
We found in 1) all possible combinations. We are told that the sum of the children’s age is equal to the house number of the house next door.

We therefore sum all the children’s ages in all the 8 combinations.
1 + 1 + 36 = 38
1 + 2 + 18 = 21
1 + 3 + 12 = 16
1 + 4 + 9 = 14
6 + 6 + 1 = 13
2 + 2 + 9 = 13
2 + 3 + 6 = 11
3 + 3 + 4 = 10

He says there is still not enough information.

The second clue is not about the house number, but the fact that even knowing the house number is not enough to calculate their age.

This means that the sum of the children’s age cannot be unique.
(If all the combinations had different sums we would have known which combination was the children’s age for that combination was identical to the house number of the neighbor).

As we can see from 2) there are two combinations that have identical summation.

6 + 6 + 1 = 13
2 + 2 + 9 = 13

3) The last hint is: «the oldest of the three plays the piano.»
Based on this hint, we know that one of the children is the oldest. In the two combinations we have, there is only one combination where one child is the oldest (in the other combination both the oldest are the same age, in fact 6 years and you have no children who are the oldest).

So the correct answer to the riddle is that the children are 2 years, 2 years and 9 years.

## Farm of wheat

Three brothers live on a farm. They agreed to buy more seeds.
Allan and Brad would go and Clint stayed home to look after the farm.
Brad bought 75 bags of wheat on the market while Allan bought 45 bags.

At home they split the sacks equally.

Clint, who stayed at home, had paid \$ 1400 for his share of the wheat.

How much did Allan and Brad receive from the money that Clint had paid, given the equal distribution of the bags?

Each brother’s portion is 1/3 (45 + 75) = 40 bags.
Clint paid \$1400, – for 40 bags, this gives a cost per bag of \$1400, – / 40 = \$35, – per bag.
Allan got 35 x (45-40) = 35 * 5 = \$ 175
Brad got 35 x (75-40) = 35 * 35 = \$ 1225

Answers will then be as follows: