I am a self-described board game nerd. Since I also like math, it logically follows that I should like math games. Likes math + likes board games = likes likes math board games.
The game Projected Marks was heavily inspired by a game in the book Math Games with Bad Drawings, by Ben Orlin, who in turn took it from Andy Juell. I highly recommend you check the book out- it includes not only nerdy games, but entertaining anecdotes and bits of knowledge as well! I’m rather fond of my copy.
Set-up: While Projected Marks isn’t exactly a board game, because it’s played on paper, it’s certainly a strategic game. To start, you will need two players, two pencils in different colours (one for each player), and a piece of paper. Draw a 5x5 grid on the paper.*
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How to play: You want to accurately predict how many numbers will be in any given row or column by the end of the game. The two players take turns to mark something in an empty square. You have two options:
You can write a number in an empty box. This number is your prediction/guess of how many numbers will be in this row or column; therefore, the highest number you can write is the amount of rows or columns (5), and the lowest number you can write is 1. Like in Sudoku, each number can only appear once in each row or column.
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□4□□□
□□□1□
5□□□□
□□□2□
Alternatively, you can mark a box with an X. This means the box is permanently empty.
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□4□□□
□□□1□
5□X□□
□□□2□
Every number (or X) affects how other predictions play out. By placing an X in the fourth row, Green has ensured that Pink’s prediction for that row (having all 5 numbers in that row) can’t come true. However, you can place multiple numbers in the same row or column. So, if we move forward a few more turns…
□□□4□
□4□□□
□□□1□
5□XX3
□□□2□
Pink now has two numbers in row #4. Green faces a conundrum: they could put a 2 in the last remaining spot, because there are two numbers in that row- but if they mark 2, there will be three numbers, so Pink would get the point. Tricky!
If Green chooses to place an X in the last spot instead, no one will get the point for that row, because no one made a correct prediction.
Later on in the game, when the board begins to fill up, a square may become unplayable: the bottom left square is impossible to fill, because 1, 2, 4, and 5 are already in its row, and 3 and 5 are in its column. In that case, you can simply put an X in it. This doesn’t count as a turn.
□□245
34X52
□□X1□
5XXX3
□5124
Play until the board is filled up, then count points. You receive one point for each row or column in which you predicted correctly.
X3245
34X52
42X11
5XXX3
X5124
First, count how many numbers appear in each column, and then circle* the correct prediction (if there is one). In this example,
column #1 has three numbers (circle the 3),
column #2 has four numbers (circle the 4),
column #3 has two numbers (circle the 2),
column #4 has four numbers (circle the 4),
and column #5 has five numbers (circle the 5).
For each circled number in your colour, you get a point.
Then, count the rows:
row #1 has four numbers (circle the 4),
row #2 has four numbers (circle the 4),
row #3 contains an illegal move which the author only just realized: there are two 1s next to each other. However, there are still four numbers, so we’ll circle the 4,
row #4 has no correct predictions,
and row #5 also has four numbers (circle the 4).
For each circled number in your color, you get a point.
*[In this diagram, circles are represented by bolding, and double circles by bolding and italics.]
X3245
34X52
42X11
5XXX3
X5124
Now we count the points. Pink has 3 points (from the columns) + 2 points (from the rows) = 5 points. Green has 2 points (from the columns) + 2 points (from the rows) = 4 points. Pink wins!
Makes sense? Hopefully - but I always read game rules through twice, to ensure I know what I’m doing before I play. If you’re still a bit uncertain, I’d recommend that!
*And why a 5x5 grid? Well, a 5x5 grid includes all the possible scores you can receive on an AP exam. Except here, a 5 and a 1 will get you the same amount of points.
As a variant, you can decide that you receive the amount of points as the number circled- so correctly guessing that there will be 5 numbers in a row/column will get you 5 points, whereas correctly guessing a 2 gets you just 2 points.
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Luisa Ensslin is a Grade 12 student in Canada. She loves all things writing, be they newspaper articles, novels, checklists, or reading things that talented people have written.