Money game and some cute little challenges

Who: J1
When: after breakfast (no school today!)
Where: dining room table
What you need: playing cards with images of money on them

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Played a cute game called '51' from RightStart Math using their US coins card deck. It was an ok game that led to a surprisingly interesting discussion.

The game in brief:

• The US coin cards show the obverse image from pennies, nickels, dimes, quarters, and Kennedy half dollars. One side of each card has two copies (two total images) of the coin, the other sides are a common pattern (so you don't know the coin when the card is turned down).
• Players are each given 3 cards
• On each turn, a player plays a card to an open stack making a total less than 52 cents, collects the stack if they have made exactly 51 cents, or plays a card to create a new stack if their coin would cause the existing stacks to overrun 51.
• At the end of the game, compare who has collected the most cards

An ok game with some strategy and some calculation practice (particularly reinforces the strategy of regrouping and number facts related to coin denominations).

Here was the fun part:

Challenge 1

At the end of one game, we had 90 cents unclaimed on the table.

I was initially surprised, thought for a moment, then realized what had happened. Questions I posed to J1 that I offer to you:

1. Why was I surprised?
2. How much did we usually have remaining on the table at the end of play?

Challenge 2

How many dollars are represented by coins in our card deck? Hint: it is an integer.

Challenge 3

What is the maximum amount that could be stranded at the end of the game? Does this depend on the number of each denomination in the pack?