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:
A man gets off the bus looking for an address and approaches a couple walking in the same direction for directions. The woman says they’re going that way and take him. Along the way the man asks if they’re related. The woman grins and says, “We’re not strangers. This man’s mother is my mother’s mother-in-law.” The man is confused but doesn’t say anything. When he gets back home he tells his wife about the conversation and she can’t figure it out either. They decide to ask their lawyer and he eventually works it out with pen and paper. How are the couple related?