[Photo from Wikipedia.]
Two of the most popular New Year’s Resolutions are to spend more time with family and friends, and to get more exercise. The 2011 Mathematics Game is a chance to do both at once.
So grab a partner, slip into your workout clothes, and pump up those mental muscles!
Here are the rules:
Use the digits in the year 2011 to write mathematical expressions for the counting numbers 1 through 100.
- All four digits must be used in each expression. You may not use any other numbers except 2, 0, 1, and 1.
- You may use the arithmetic operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial). You may also use parentheses, brackets, or other grouping symbols.
- You may use a decimal point to create numbers such as .1, .02, etc.
- Multi-digit numbers such as 20 or 102 may be used, but preference is given to solutions that avoid them.
Bonus Rules
You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.
You may use multifactorials:
- (n!)! = a factorial of a factorial, which is not the same as a multifactorial
- n!! = a double factorial = the product of all integers from 1 to n that have the same parity (odd or even) as n
- n!!! = a triple factorial = the product of all integers from 1 to n that are equal to n mod 3
[Note to teachers: The bonus rules are not part of the Math Forum guidelines. They make a significant difference in the number of possible solutions, however, and they should not be too difficult for high school students or advanced middle schoolers.]
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