You are your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.
Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge!
Each troll, quite rightly, insists that you pay a troll toll.
Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.
How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?
Hint: At each bridge you lose half of your cakes, but get one back.
At each bridge you are required to give half of your cakes, and you receive one back.
Which leaves you with 2 cakes after every bridge.
If you roll two normal 6-sided dice, the probability of rolling a total of 7 is 1/6.
What would the probability of rolling a total of 7 be if both dice were 7-sided instead?
How about a 8-sided dice? 9-sided? 10-sided?
[Ref: ZBMA] © Kevin Stone
Hint: How many possible ways are there to make 7?
There are 49 possible combinations when rolling two 7-sided dice.
There are still six ways of making a total of 7, therefore the probability is 6/49.
In each scenario, there are still only six ways of making a total of 7, the only thing that changes is the number of possible combinations.
7-sided > 6/49
8-sided > 6/64
9-sided > 6/81
10-sided > 6/100
My bath has two taps and a plug hole.
The cold tap on its own fills the bath in 18 minutes, the hot one in 15 minutes.
The plug hole can drain the bath in 10 minutes with the taps off.
How long will the bath take to fill if I leave both taps on with the plug left out?
[Ref: ZCSZ] © Kevin Stone
Hint: How many baths could the cold tap fill?
Answer: 45 minutes.
In 24 hours:
the cold tap could fill 80 baths
the hot tap could fill 96 baths
the plug could drain 144 baths
Therefore, in 24 hours, we have 80 + 96 - 144 baths full = 32 baths.
Therefore each bath would take 45 minutes to fill.
If a hen and a half will lay an egg and a half in a day and a half, how many eggs would six hens lay at the same rate in six days?
[Ref: ZPZF] © Kevin Stone
Hint: Think about three hens first.
A hen and a half will lay an egg and a half in a day and a half.
So three hens will lay 3 eggs in a day and a half.
So six hens will lay 6 eggs in a day and a half.
Therefore six hens will lay 24 eggs in a 6 days.
What is the smallest integer, which, when multiplied by 2 gives a number consisting of only 8's?
[Ref: ZNJR] © Kevin Stone
Hint: Remember that you're after the smallest one that works.