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Answers to Brainteasers from pgoh13.com

How many faces can you see? 10

Mensa brainteasers

Number 1:
The answer is 5.60£.
17 shirts at 8£ each = 136£
17 shirts plus 85 shirts equals 102 shirts
102 shirts at 6£ = 612£
612£ - 136£ = 476£
So the 85 shirts were sold for 476£
Which means that the sale price of each shirt was 476/85 = 5.60£

Number 2:
The answer is 2.4km
Let's say x km is the answer (x representing the unknown)
x km times 60 mins divided by 40km minus 2 mins = x km times 60 mins divided by 90km
So 1.5x minus 2 = 2x divided by 3
2x = 3 times (1.5x minus 2)
2x = 4.5x minus 6
2x minus 4.5x = minus 6
-2.5x = -6
2.5x = 6
Therefore x = 2.4km

Number 3:
The answer is 40mph
Let's say the distance is x miles (x representing the unknown)
Total time for the two trips (in hours) is x/50 plus x/33.33 which is the same as 2x/100 plus 3x/100 which will give you 5x/100 or x/20 hours
Since the total distance for the two trips is 2x miles, the average speed for the entire journey (to and fro) is 2x divided by x/20 which will give you 40x/x equals 40mph.
The answer is 40mph

Number 4:
The answer is 50 miles
Let's say the whole distance to be travelled is x miles - which means he has travelled only (x - 10) miles since there is still 10 miles to be travelled
1st hour: Distance travelled in the lst hour is x/3 while distance remaining is 2x/3 miles
2nd hour: Distance travelled in the 2nd hour is 2x/9 while distance remaining is 4x/9 miles
3rd hour: Distance travelled in the 3rd hour is x/9 while distance remaining is x/3 miles
4th hour: Distance travelled in the 4th hour is x/6 while distance remaining is also x/6 miles
This means that x/6 = 10 and therefore x = 60
So the total distance is 60 miles and the car has travelled 50 miles.
To check if our answer is correct, let's substitute x with 60 in the above assumptions:
1st hour: Distance travelled in the lst hour is x/3 = 20 miles
2nd hour: Distance travelled in the 2nd hour is 2x/9 = 13 1/3 miles
3rd hour: Distance travelled in the 3rd hour is x/9 = 6 2/3 miles
4th hour: Distance travelled in the 4th hour is x/6 = 10 miles
Total: 50 miles

Cheryl's birthday puzzle

The expected answer is July 16.
Alex Bollos explains it here.
However mathematician James Grime, while agreeing on July 16, says an alternative answer (August 17) is possible. You can find his argument here.

How sharp are your eyes?

1. C is in the 7th line, just after the halfway mark.
2. 6 is in the 4th line, the very first letter.
3. N is in the first line near the end.

"Number of legs in the bus" riddle

The 10,990 legs can be accounted for as follows:
There are 7 girls so there are 7 x 2 legs =        14 legs
Each girl has 7 backpacks. So there are 7 x 7 = 49 backpacks.
Each backpack has 7 big cats so 49 x 7 = 343 big cats.
343 big cats x 4 legs =
    1,372 legs
Each of the 343 big cats has 7 kittens so 343 x 7 = 2,401 kittens.
2,401 kittens x 4 legs =
  9,604 legs
TOTAL NUMBER OF LEGS = 10,990 legs

Riddle of the 68 camels

Mathematically, and on the surface, there is no way one can divide the 68 camels in the way the father wanted. What the lawyer did was to "lend" 4 of his own camels to the 68 making 72 camels in all. Now half of this is 36, one-third is 24 and one-ninth is 8 making a total of the father's 68 camels. So he gave 36 of these to the eldest, 24 to the second and 8 to the youngest. He then takes his 4 camels back home with him! The sons won't complain neither for each of them would have got more than what he was really entitled to!
I have since come across another such puzzle. Here it is not 68 camels but 17 camels that have to be divided in the same proportions as above. You should be able to solve this easily now.
And with the same logic you'll be able to resolve Ali Baba's enigma of dividing his 39 camels among four sons so that the eldest got half, the second a quarter, the third an eighth and the youngest a 10th. In this story it was not a lawyer but a stranger who came riding along on his camel that helped them solve their problem before riding off and leaving them completely stunned.
Hey, there is a mathematical explanation behind all this. But I'll leave this to your maths teacher!

3 men in a motel (the missing dollar)

This brainteaser is an example of a false problem. You cannot add the 27$ to the 2$ as the 2$ that is now with the bellboy is actually part of the 27$ they finally paid for the room!
So there is no question of 1$ being "missing"!
In fact you have to add the 27$ to the 3$ that the men got back. Although the 3 men paid 27$ they didn't give that money to the hotelkeeper. The fact is that the 2$ extra that they paid is with the bellboy.
So the original 30$ is distributed as follows:
hotelkeeper 25$, bellboy 2$, 3 men 3$.
Beware of ostensible reasoning!

Riddle of the 4 persons crossing a lake

A Nigerian village woman (the 1st person) with her child (the 2nd person) at her back and her healthy twins (the last two persons) inside her womb!

"Names are not what they claim to be!"

1) How long did the Hundred Years War last?
- 116 years
2) Which country makes Panama hats?
- Ecuador
3) From which animal do we get catgut?
- Sheep or horses
4) In which month do Russians celebrate the October Revolution?
- November
5) What is a camel's hair brush made of?
- Squirrel fur
6) The Canary Islands in the Pacific is named after what animal?
- Dogs
7) What was King George VI's first name?
- Albert
8) What color is a purple finch?
- Crimson
9) What is the color of the black box in a commercial airplane?
- Orange

Answers to the 12 brain-teasers

1. Since half of the 97% wear two earrings and the other half don't wear a single earring it is as if every single one of them wears one earring. And since the other 3% of the women really wear one earring each the total number of earrings is 800.
2. Since there were only two barbers they must have cut each other's hair. The second must have his hair cut by the first!
3. He had already put sugar in his coffee before he noticed the fly!
4. They are triplets.
5. There were only three persons at the table comprising a grandfather, his son and his grandson.
6. Mount Everest, of course. It was always there!
7. In a dictionary.
8. Three.
9. A leaf.
10. Put yourself back to back of each other.
11. An echo.
12. He was in a merry-go-round.