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# Triangle: A new math card game

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!

1. Terri

Excellent game creation. What a great way for a child to express some creativity and originality. I’m glad to hear he’s working with you. I think I might mention this to Nathan. It might be something fun to play on vacations when all you can carry is a deck of cards because TSA will probably one day claim that a D6 is a weapon.

2. Jason Buell

Great game. Sounds like good fun.

For the 2 player – Perhaps a SET like setup where you lay out x number of cards face up and a player calls out when he/she finds a group of cards that will work for that row. The heads up competition is more daunting though but it might be fun for older kids who are fairly evenly matched. My main reservation with the take turns variation is the time I would spend going through the many combinations in my head while my opponent is just sitting and watching. It seems like it’d drag a little, like playing scrabble with my dad.

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Dan

Thanks for the suggestions, Jason! I just tried a variation on your SET-like suggestion with some students yesterday, except we ended up going more Boggle-ly. It went really well.

My latest idea is even more boggle-ly: put down nine cards in a 3 by 3 array plus a target card. Then you write down as many equations as you can that use a connected series of cards (connected meaning adjacent horizontally, vertically, or diagonally). There just needs to be a good way of scoring what each equation is worth. It seems like the longer it is, and the more it uses “hard” operations like division, but more points the equation is worth.

3. Anusha

What a great game!

For the 2 player version — what about not dealing out cards, but each player has to pick as many cards as is required by the next row (first time, each player needs to pick up two, once the second row is finished, each needs to pick up 3 at a time etc). If they are not able to complete the row, they wait for their next turn. The one with the most cards in their hand (or the highest additive value of cards in their hand) loses the game. The end of the game could either be reaching 5 rows or end of deck. We may need more than one deck of cards for this version though.

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Dan

Thanks for the thought, Anusha. I’ve been messing with this idea (that you’re trying to minimize your number of cards at the end), and I think it could work. Just involves lots of practice games…

4. Jason Buell

I think last time I also suggested a SET-like setup. Clearly I’ve been playing that game too much. I was thinking about this last night and perhaps a slap jack setup might be fun. So for each row you lay out all the cards but one and the flip the deck one at a time. You slap the card if it works and then need to explain your equation. If it doesn’t work then the other player gets to lay down the next three cards without competition. (or something…haven’t thought that part out).

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5. John Golden

These are verrry cool.

I was wondering if a multi-person game could be played like rummy. Each turn a player draws a card, or picks up the top discard, and can play an equation. But only one equation of each length. So if the target is 4, you could play 4, 7-3, (2+10)/3,…

I think the benefit of not having to play the lengths in succession and seeing the discard pile might help in the non-solitaire format. I am a little crazy about rummy, though.

Even Go Fish might work here, though.

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