# Triangle: A new math card game

November 30, 2010

A 10-year-old I meet with greeted me yesterday by telling me that he’d had an idea for a game called “Triangle” right before going to bed. He described the basic premise, and we toyed with different ideas for game play. As we worked, I mentioned my three guidelines for inventing a game:

1. It should have a clear goal.
2. It should have clear rules.
3. It should be fun.

We came up with a decently good version of Triangle. Since then, I’ve spent a little time tweaking, and I think I’ve got a two pretty good versions. However, I’m missing one thing: how winning works. The solitaire version, at least, is worked out.

#### Triangle Solitaire

Start by dealing a card face up.

That card is the target card. You start with two cards in your hand, and take cards one at a time from the deck. Your goal is to take two that add, subtract, multiply, or divide to make the target value. For instance, by the time I had a hand of five cards, I was ready to make my play:

since 8 divided by two is four. Now I continue to draw cards until I can make an equation to complete the next row of the triangle. In this case, it’s

which is good, since (7 * 1) – 3 = 4. (Note: you’re allowed to put parentheses wherever you want.) Next I’m trying to use four cards to complete the next row. I keep drawing till I find

I count jacks as 11, queens as 12, kings as 13, and aces as 1 or 14. So this turn reads

(11 – 9) + (2 * 1) = 4. I pick four cards from the deck, and my final play is a row of five:

Here my play reads ((13/13)+7) divided by (11-9) = 4. After this you can keep drawing and doing more rows. The goal is to do as many rows as you can.

VARIATION (Square): You play as above until you make a row of seven. Then in subsequent rows you shorten them, making rows of 6, 5, 4, etc. until you’re down to a row of one card, which must match your original card. Bonus points if there’s a way to use the remaining three cards to equate to the top card as well.

#### 2-player Triangle

I’m decently satisfied with the solitaire game. But what about the two player version? I keep trying different things, but nothing is quite right. My best idea right now is that you essentially play the solitaire version against each other, taking turns. You start by dealing a target card (the 3 of spades, below), and three cards to each person. You can either draw a card or play your next row. (Here’s the game after each player has played one row. One player has 6/2 = 3, the other has 8 – 5 = 3.)

If you ever use up all your cards, you get to immediately pick three more. The game ends whenever someone reaches some agreed upon row–say the five card row (or it ends when you run out of cards in the deck).

I think that might work. I’m still having trouble getting it totally straight. Let me know if you have ideas!

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