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In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly?
Escape to answer without getting tricked!
What was the game?
There is absolutely no way that somebody has guessed 3 correctly since if 3 are correct then 4th has to be correct. Hence, nobody guessed 3 correctly.
So number of people with all 4 guess correct is equal to 123 - 43 - 39 - 31 = 10.
10 people guessed all the 4 fruits correctly.
A rich merchant had collected many gold coins. He did not want anybody to know about them.
One day, his wife asked, “How many gold coins do we have?”
After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers.”
The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold coins they have?
Here are mathematical steps to find those!
What was that clue?
Since when divided into 2 unequal numbers difference won't be 0. Let x and y be the 2 unequal numbers.
As per merchant,
32 (x - y) = x^2 - y^2
32 (x - y) = (x - y) (x + y)
Dividing both sides by (x - y) which is non zero as x is not equal to y,
32 = x + y
x + y = 32.
Let's verify with x = 30 and y = 2. So 32 (x - y) = 32 ( 30 - 2) = 896. And x^2 - y^2 = 30^2 - 2^2 = 900 - 4 = 896.
Hence, Merchant had 32 coins in total.
Whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):
1 2 3 5 7 11 13 17 19
Is it?
Find the possibility here!
What was the task given?
That's impossible task. All the listed prime numbers sums together to 78. For square to be magic, sum of each row & column must be equal. In this case, it should be 78/3 = 26.
For sum of 3 to be even, 1 must be even & other 2 odd (or all even). All 3 odd can't sum even.
In listed prime numbers there is only 1 even number i.e.2. Hence, for other 2 rows/columns we can't have even sum.
There is an Island of puzzles where numbers 1 - 9 want to cross the river.
There is a single boat that can take numbers from one side to the other.
However, maximum 3 numbers can go at a time and of course, the boat cannot sail on its own so one number must come back after reaching to another side.
Also, the sum of numbers crossing at a time must be a square number.
You need to plan trips such that minimum trips are needed.
This should be that minimum number!