Brain Breakers 2

Missing Numbers

Every Man's Dream

Missing Numbers 2

A Taste for Literature

Every Man's Dream

The problem presented here sounds like an old-fashioned fairy-tale, and that's just - however unexpected - what the answer entails.

The Sultan of Khardar has fourteen wives. But he has only one five-person bed, so only four wives can sleep with him each night. However, the Sultan is a righteous man and changes the combination every night.

How many nights can the Sultan change combinations without repeating a combination?

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Ask Archimedes

1. Here we have two glasses of the same size and content. One glass is filled to the rim with water. In the other glass we first place a wooden ball, and then we fill it to the rim with water. This wooden ball floats in the water. Which glass is heavier, the glass with just water, or the glass with the floating wooden ball?

2. In a bowl of water floats a smaller container which is filled with marbles. I add so much water to the bowl that it comes to the rim. The question here is: What happens to the water level if I take a marble from the container and drop it carefully into the bowl of water: will the water level rise or fall?

3. In a bowl I put an ice cube and fill the bowl to the rim with water. What would happen to the water level when the floating ice cube is melted?

4. This time the ice cube is attached to the bottom of the bowl, I fill the bowl to the rim with water. What will happen with the water level when the ice cube is melted?

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Multiple Choice?

An Englishman and a Japanese man are on a safari trip, when they encounter a fierce lion. Immediately the Japanese sits down on the ground and puts on his running shoes. "Do you think you can outrun a lion?" taunts the Englishman.

"Yes, I can with running shoes..."
"No, but when I sit still the lion will not ..."
"There's no need to run, lions do not attack ..."
"I don't have to outrun the lion ..."

What was the Japanese man's answer, and why?

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More Calculations

Every week my son Tommy saves a 1ct piece, a 5ct piece and a 10ct piece. Every time he has saved a round-figure amount of Uro's, I will give him a bonus of one Uro. The current worth of the Uro is 100ct. How long does Tommy have to save before he gets his first bonus?
A farmer and his dog are heading for home. They pass a road sign which indicates that they still have 20 miles to go. The farmer is travelling at 5 miles an hour. His dog, who knows the way home well, runs ahead at 10 miles an hour. However, when he reaches home he immediately turns back towards the farmer. When he arrives back at his master, he gets a pat on the head and then he starts to run home again. He does this until the farmer reaches his house. What distance does the dog run?
What came first: the chicken or the egg? I suppose we will never know, but maybe you can solve the next one. If one-and-a-half chickens lay one-and-a-half eggs in one-and-a-half days, how many eggs do three chickens lay in one week?

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A Taste for Literature

I noticed that a bookworm had eaten a passage through my favourite trilogy, from the first page of part one to the last page of part three. Feeling sympathetic towards this fellow book lover, I decided not to kill the worm and to leave him to devour other great works. The book-block of each part is 3 cm thick, the covers are 0.3 cm.

Can you calculate the length of the passage eaten by the worm?

Tri	lo	gy

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Missing Numbers 2

		00
	10	.	21
00		13		00

		00
	17	.	11
00		14		00

In these triangles the middle number of each side is the sum of the missing corner numbers.

Can you find the missing numbers?

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Missing Numbers

.	7	.
10	.	21
.	24	.

.	16	.
21	.	17
.	22	.

In these squares the middle number of each side is the sum of the missing corner numbers.

Can you find the missing numbers?

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Counterfeit Coins

Situation I:
After a dubious transaction you have received payment of ten sacks of gold coins, containing one hundred coins each. Your partner isn't exactly reliable, and somebody warned you that one of the sacks would contain coins of a lower weight than they should be. The coins in this sack weigh 9 grams instead of 10 grams. The transaction takes place at the Central Railway Station in the middle of the night, where luckily there is a weighing-machine that can weigh with a precision of a tenth of a gram. The problem is that you have to sort this out on the spot, and you have only one dime to use on the weighing-machine.

Situation II
What will you do in the following case:
Now, some or all of the sacks may contain bad coins, each weighing 9 grams. You still are allowed to weigh once. How you do proceed?

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The Hole in Sphere

Old Boniface he took his cheer,
Then he bored a hole through a solid sphere,
Clear through the centre, straight and strong,
And the hole was just six inches long.

Now tell me, when the end was gained,
What volume in the sphere remained?
Sounds like I haven't told enough,
But I have, and the answer isn't tough!

So what is the remaining volume?

Answer

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Dog's Mead

This classic crossword puzzle by James Fixx concerns a farm that has been in the Dunk family for some years. A part of the farm is a rectangular piece of ground known as Dog's Mead.

Additional background information:
The year is 1939, 4840 square yards is one acre, 4 rods is one acre. 20 shillings = 1 pound sterling

mead.gif (3405 bytes)

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Across
1. Area in square yards of Dog's Mead.
5. Age of Martha, Father Dunk's aunt.
6. Difference in yards between length and breadth of Dog's Mead.
7. Number of rods in Dog's Mead times 8 down.
8. The year the Dunks acquired Dog's Mead.
10. Father Dunk's age.
11. Year of Mary's birth.
14. Perimeter in yards of Dog's Mead.
15. Cube of Father Dunk's walking speed in mph.
16. 15 across minus 9 down.

Down
1. Value in shillings per rod of Dog's Mead.
2. Square of the age of Father Dunk's mother-in-law.
3. Age of Mary, Father Dunk's other daughter.
4. Value in pounds of Dog's Mead.
6. Age of Ted, Father Dunk's son, who is twice the age of his sister Mary in 1945.
7. Square of the breadth of Dog's Mead.
8. Time in minutes it takes Father Dunk to walk 1 1/3 times around Dog's Mead.
9. The number which, multiplied by 10 across, gives 10 down.
10. See 9 down.
12. Addition of the digits of 10 down plus 1.
13. Number of years Dog's Mead has been in the Dunk family.

The Train

The train arrived on time (for once) and everyone boarded. Henry the driver was 45 and wore green socks. Each passenger had a different age (and different to Henrys). Andrew was twice the age of June who is in first class wearing a yellow hat. Nancy was younger than Henry and sat in second class knitting a red jumper. Susan's age was the sum of the two youngest passengers who were in their blue school uniform. William was with his purple-hatted mother Iris in second class. Every first class passenger had an odd age, every second class passenger an even age. Richard sat in first class with the oldest passenger who had white hair. Iris is 14 years older than Nancy and 5 years younger than Richard. Susan is sat with Andrew who was in his grey suit. Richards age is half the sum of Iris and Nancys ages. Everybody was born in the last 50 years. Do tell me now, what the colour of the train is?

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