You have ten boxes and an electronic weighing machine. In those ten boxes, you have chocolates. Each chocolate weigh 20 grams. But in one box the chocolates are defective and each weigh 19 grams exactly.
Now you can weigh in the electronic weighing machine but you can use that machine just once. How will you find out which box has the defected chocolates.
If you are thinking to hold one chocolate from each box in hand and then balancing weight in bare hands, you are thinking all wrong.
Let us begin by labelling boxes as 1, 2, 3 and so on till 10.
Now pick one chocolate from box 1, two chocolates from box 2, three from box 3 and so on. In total, you will have 55 chocolates now. (1 + 2 + 3 + ..... + 10)
The ideal weight of the chocolates should be 55 * 20 = 1100. However, somewhere in there are the defected chocolate/s.
You can judge that clearly by noting down the result of 1100 - total weight of chocolates. If the weight is less than 1 gram, the defected box is box 1, if the weight is less than 2 grams, the defected box is box 2 and so on.
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
It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 123-43-39-31 = 10 people have guessed four fruits correctly.
You are stuck with the pirates who might even kill you on board. They give you a chance to survive. There are hundred black rocks and hundred red rocks. There are two empty sacks which are labelled as heads and tails respectively. You have to divide the rocks in two bags as per your wish. Then a fair coin will be flipped. If its heads, you will have to pick a rock on random from the sack labelled heads and if its tails, you will pick up from the tails sack. If you pick up a black rock, you will be freed and if you pick up a red rock, you will be killed.
How will you distribute the rocks so that your chances of survival are the best?
You can see five identical squares made with blue matchsticks in the given figure. You have to make them six identical squares instead. To do that, you are only allowed to move three matchsticks. How will you achieve the desired result?