It is one of those problems which will keep you thinking for much time. But did you consider the fact that that the number of pennies are not told and the question asks if the stack will fit the room or not.
Also the size of the room is not mentioned and it is left to your intuition. Now consider the Empire State Building which is 102 stories tall or say 100 story tall on a rough note. Now that is hundred times more than an ordinary room measured on the inside. Now you will have to break the skyscraper-high column of pennies into about a hundred floor-to-ceiling-high columns. Now the question becomes if you can fit approximately hundred floor-to-ceiling penny columns in a room?
Surely! It will be just a ten by ten array of penny columns. Of course, every room will have enough space to set hundred pennies flat on the floor.
The toothpicks in the picture have been arranged to form a donkey shaped figure. You have to move two matchsticks in a way that the entire shape is rotated / reflected while being intact. Also, you can't change the tail's direction it should be pointing up.
The world is facing a serious viral infection. The government of various countries have issued every citizen two bottles. You as well have been given the same. Now one pill from each bottle is to be taken every day for a month to become immune to the virus. The problem is that if you take just one, or if you take two from the same bottle, you will die a painful death.
While using it, you hurriedly open the bottles and pour the tablets in your hand. Three tablets come down in your hand and you realize they look exactly the same and have same characteristics. You can’t throw away the pill as they are limited and you can’t put them back or you may put it wrong and may die someday.
How will you ensure that you are taking the right pill?
You must put labels on the tablets as A and B before using. In that case, if you pour tablets together, you will get 3A, 2A 1B, 1A 2B or 3B. If they are from the same bottles you can take one from another bottle and save the remaining two for another day. If you get two from same and one from other, you can draw one from another bottle and you will have two pairs of which you can eat one and save the other.
Suppose there is a Christmas tree and four angels are sitting on it amidst the other ornaments. Two of them have black halos and two of them have white halos. No body among them can see above their head. Angel A is sitting on the top branch and can see angels B and C sitting below him. B can see C who is sitting in a branch lower than his. Angel D is at the base of the tree and can't be seen due to the branches in between. Also, he can't see anybody as well.
If they are asked to guess the color of their own halo (they dont know that), who do you think will be able to deduce and speak up first with a right answer?
Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.
So either A or B will speak up first depending on the situation.
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
As shown in picture, there are four gears with the following specification
* Gear A has 60 teeth
* Gear B has 40 teeth
* Gear C has 20 teeth
* Gear D has 60 teeth
* Every minute, Gear B makes 15 complete turns.
You have been given three jars of 3 liters, 5 liters and 8 liters capacity out of which the 8 liters jar is filled completely with water. Now you have to use these three jars to divide the water into two parts of 4 liters each.
How can you do it making the least amount of transfers?