2026 Mathematics Game

Now that we’re a few months into the year, many of our New Near’s resolutions have probably fallen by the wayside. It’s inevitable, according to Mark Twain, that we shall “cast our reformation to the winds and go to cutting our ancient shortcomings considerably shorter than ever.”

But there is one resolution that I enjoy keeping—the resolve to play more math.

My favorite way to celebrate at any time of the year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular resolutions: spending more time with family and friends, and getting more exercise.

So grab a partner, slip into your workout clothes, and pump up those mental muscles!

Rules of the Game

Use the digits in the year 2026 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.

• You must use all four digits: 2, 0, 2, and 6. You may not use any other numbers.

• You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.

• You may use a decimal point to create numbers such as .2, or you may create multi-digit numbers such as .02 or 20 or 202.

While this year offers more options than many recent years, we’ll need plenty of arithmetic tricks to create variety in our numbers. Experiment with decimals, two-digit numbers, and factorials. Remember that dividing (or using a negative exponent) creates the reciprocal of a fraction, which can flip the denominator up where it might be more helpful.

My Special Variations on the Rules

• Challenge yourself: Keep the year digits in 2-0-2-6 order, if you can. And stick to the single-digit numbers as long as possible, leaving multi-digit numbers like .02 or 20 as a last resort.

• You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.

• You may also use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. But save it until you’ve tried everything else. I feel much more creative when I can wrangle a solution without invoking double factorials.

Clarifying the Do’s and Don’ts

Finally, here are a few rules that players have found confusing in past years.

These things ARE allowed:

• You must use each of the digits 2, 0, 2, 6 exactly once in each expression.

• For this game, 0! = 1 and 0^0 = 1.

• Unary negatives count. That is, you may use a “−” sign to create a negative number.

• You may use (n!)!, a nested factorial, which is a factorial of a factorial. Nested square roots are also allowed.

• You may use n!!, a double factorial, which is a factorial that uses only the numbers with the same parity (odd or even) as n.

These things are NOT allowed:

• You may not write a computer program to do the puzzle for you. Or at least, if you do, PLEASE don’t ruin our fun by telling us all the answers!

• You may not use any exponent unless you create it from the digits 2, 0, 2, 6. You may not use a square function, but you may use “^2”. You may not use a cube function, but you may use “^(2+0!)”. You may not use a reciprocal function, but you may use “^(−0!)”.

• While we do allow the square root function, you must create any other roots from the digits 2, 0, 2, 6. For example, to take the cube root of a number, use the radical symbol along with (2+0!) to mark it as cube root.

• “0!” is not a digit, so it cannot be used to create a base-10 numeral. You cannot use it with a decimal point, for instance, or put it in the tens digit of a number.

• The decimal point is not an operation that can be applied to other mathematical expressions: “.(2+0!)” does not make sense.

• You may not use the integer, floor, or ceiling functions. You must “hit” each number from 1 to 100 exactly, without rounding off or truncating decimals.

Helpful Links

• Mathematics Game Worksheet
  For keeping track of which numbers you’ve solved.

• Mathematics Game Manipulatives
  This may help visual or hands-on thinkers.

For more tips, check out this comment from the 2008 game. And Heiner Marxen has compiled hints and results for past years (and for the related Four 4’s puzzle).

Dave Rusin describes a related card game, Krypto, which is much like my Target Number game.

Alexander Bogomolny offers a great collection of similar puzzles on his Make An Identity page. And Pat Ballew takes a brief look at the history of such arithmetic puzzles.

I love the year game! It’s new every time, and such a fun way to build number skills. I do hope you give it a try.