Step1. Lets say y = x
Step2. Multiply through by x xy = x2
Step3. Subtract y2 from each side xy - y2 = x2 - y2
Step4. Factor each side y(x-y) = (x+y)(x-y)
Step5. Divide both sides by (x-y) y = x+y
Step6. Divide both sides by y y/y = x/y + y/y
Step7. And so... 1 = x/y + 1
Step8. Since x=y, x/y = 1 1 = 1 + 1
Step9. And so... 1 = 2
Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules
There is a 30km long bridge. The bridge can only support up to a weight of 2000 kg. A car that weighs 2000 kg needs to cross that bridge. When the car has reached midway of the bridge, a bird comes and sits on top of the car. The bird weighs 300 grams.
Now, does the bridge breaks down at this point of time or not?
Rohit is on his way to visit your Grandma, who lives at the end of the state.It's her birthday, and he want to give her the cakes that he has made.Between his place and her grandma house, he need to cross 7 toll bridges.
Before you can cross the toll bridge, you need 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 rohit have to carry with him so he can reach his grandma home with exactly 2 cakes?
Two brothers have developed differences among themselves and thus want to part ways. The problem is that they have one big land that is irregular in shape. Both of them want an equal share which is fairly impossible as there is no way that land could be divided in equal halves due to irregularity in the shape.
The wisest man of the village is called who tells a way in which both of them will be happy even though the land might not be divided into exactly equal halves.
He simply suggested that one of the brothers will be allowed to divide the land but he must take into consideration that it will be the other one who will have a choice of selecting his land between the two halves first.
I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy?
A great meeting is held by a great logician where all the other logicians are called upon. The master logician takes them in a room and makes them sit in circle. A hat is placed on each of their heads. Now all of them can see the color of hats others are wearing but can’t see his own. They are told that there different colors of hats.
The master logician explains that a bell will be rung at regular intervals and the moment when a logician knows the color of his hat, he will leave on the next bell. If anyone leaves at the wrong bell, he will be disqualified and sent home.
All of them are assured of one thing that the puzzle will not be impossible for anyone of them. How will they manage the situation?
The first step that they will take will be a leap of logic. What it means is that they will deduce that every color must appear twice at least. Why? Because the master logician has assured them that the puzzle will not be impossible for anyone of them. And if a color appears only once in the circle, the person wearing it will have no clue about that color which will not be fair for him.
Then the logicians will follow the same and look for all the colors of hats in the circle. If one of them sees a color just once, he can safely assume that he is also wearing the hat of the same color as by leap of logic, no color can appear just once. Thus when the bell is rung, he will leave.
In the similar fashion, if anyone sees another color just once, he can determine that he is wearing the hat of the same color and will leave when the bell rings or will be disqualified and sent home. Unvaryingly, if a color is seen twice, they will be eliminated after the first bell. Hence, there must be at least three hats of any of the remaining color.
Assume that you are sitting in the circle and you don’t see a color once but see it twice. Then if they were the only two hats of the same color, the logicians must have left at the first bell already. But they did not. Which means that there are three hats of that color and you are wearing one. Thus you will leave after the second bell.
A guy claims to do the following thing. He puts a coin in a glass bottle. Then, he shuts the mouth of the bottle with the help of a cork. Now he manages to remove the coin out from the bottle without taking out the cork or breaking the glass bottle.
In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?
The answer is 2. First, divide the coins into 3 equal piles. Place a pile on each side of the scale, leaving the remaining pile of 3 coins off the scale. If the scale does not tip, you know that the 6 coins on the scale are legitimate, and the counterfeit is in the pile in front of you. If the scale does tip, you know the counterfeit is in the pile on the side of the scale that raised up. Either way, put the 6 legitimate coins aside. Having only 3 coins left, put a coin on each side of the scale, leaving the third in front of you. The same process of elimination will find the counterfeit coin.
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