Alfred is at the bank to cash his $200 check. He tells the cashier he would like some one dollar bills, ten times as many two dollar bills and the rest in fives.
How many of each denomination does the cashier need to give Alfred?
We know that in order to give the rest of the amount in fives, the sum of the one and two dollar bills needs to be divisible by five (i.e. end in 0 or 5).
If we start with a single one dollar bill, we’d need ten two dollar bills to satisfy the request, making $21. But we need a sum that is divisible by 5. So we keep going up, like so:
This word starts with the same letter it ends with and there are two of the same along the way. There is another pair and one each of two more, just to make you smile. What is the word?
Giggling. It starts and ends with ‘g’ and there are two more ‘g’s in the middle. It also has a pair of ‘i’s and one ‘l’ and ‘n’. Plus, giggling makes you smile ;)
A man owed his friend $63 and repaid him the exact amount in cash without using coins or $1 bills (no online transfers, checks, credit cards or any other tricks) and without requiring change. How did he do it?
You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls and instructs you to divide the 100 marbles into the two bowls. You can divide them however you want as long as all the marbles are in the bowls. You will be blindfolded and the bowls and marbles will be thoroughly mixed. You will then choose a single marble from one of the bowls. If the marble is white, you live. Black and you will be put to death.
How do you divide the marbles up so that you have the greatest probability of choosing a white marble?
Place one white marble in one bowl and place the rest of the marbles in the other bowl (49 whites, and 50 blacks).
This way you begin with a 50/50 chance of choosing the bowl with one white marble and living. Even if you choose the other bowl, you still have an almost 50% chance of picking one of the 49 white marbles. There are no guarantees in life, but this gives you the best change of surviving.