There are Brown and Black cows. In five days four black cows and 3 brown cows give as mush as milk that four brown cows and 5 black cows give in four days. If the black cow gives 10 liters of milk per day, how
many liters of milk the Brown cow will give in one day?
Three tap together drain a complete tank in 5 hours. If first drains this tank in 10 hours alone, then minimum hours taken by second tap will be (in any condition)
One hundred prisoners are lined up, one behind the other, all facing forward. On each prisoner's head is a hat, either red or black. Each prisoner can see the hats of all the people in front of him, but he cannot see his own hat and he cannot see the hats of the people behind him. Starting with the prisoner in the back of the line (the one that can see all 99 other prisoners), the prison warden asks the prisoner what color hat he is wearing. Each prisoner can hear the guesses of all of the prisoners behind him. If a prisoner correctly guesses his hat color, he is set free. If he guesses wrong, he is executed.
The prisoners are allowed to agree in advance on an algorithm to use, and you can assume that they all agree to follow the agreed-upon algorithm. The prisoners are NOT allowed to provide each other with any additional clues once the hats are placed on their heads. (For example, tapping shoulders or modulating their voices are not allowed.) The only information each prisoner has is the guesses for the prisoners behind them, and the hats on the prisoners in front of them. Design an algorithm for the prisoners to follow that saves the most prisoners from execution. What is the maximum number of prisoners you can guarantee to save?
Mathematics has 25%formulas, 25%proofs and apply 25%thinking and 25%efforts.
In real life situations proofs are nothing but already existed stories(we know the solutions from all experienced people).
formulas are nothing but goals. we have so many goals b