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:
Twenty one points divide and dance,
Twirling and leaping about,
Ladies, Romans and knights of France,
Craving a victor’s rout,
Wrought of wood, ivory or bone,
An exciting yet vicious pursuit,
Ancient, forbidden and crooked,
All in search of the loot.
A die. The standard die has 21 pips (or points), divided up on the six sides of the die which dance around when rolled. Ladies, knights and Romans all played dice as a pastime (though not together). Dice can be made of wood, ivory and bone, among other materials. Dice have been used in Asia since before recorded history and many governments tried unsuccessfully to outlaw the game. Professional gamblers were common and often used loaded dice. Desperate German chaps even bet their own liberty on a single roll of the dice.