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2018 Mathematics Game

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Use the digits in the year 2018 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and !! (double factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100.
  1. All four digits must be used in the expression.
  2. Only the digits 2, 0, 1, 8 may be used.
  3. Multi-digit numbers such as 20, 210, or .02 will be accepted this year. Note that 0.02, while equivalent to .02, would not be acceptable since only one 0 is available this year.
  4. The square function may NOT be used. Nor may the cube, raise to a fourth power, or any other function that raises a number to a specific power. For example, (1 + 8)^2 - 0! is an acceptable way to write 80, because ^ is an acceptable operation and it uses exactly the digits 1, 8, 2, and 0. But 8^2 + 2 + 1 + 0! is not an acceptable way to write 68, because "^2" is not an acceptable operation, and there are not two 2's available. Similarly, 2^3 + 8 - 1 - 0! would not be an acceptable way to write 14 since "^3" is not an acceptable operation.
  5. Multifactorials other than the double factorials may NOT be used this year. I enjoyed exploring them in previous years but many people felt they took away some of the challenge, and they were very hard to read. If you're curious about double factorials (!!), please explore the article about them on Ask Dr. Math.
  6. The integer function may NOT be used. Nor may the round, floor, ceiling, or truncate functions.
  7. Remember that 0! by definition is equal to 1. See Dr. Math's answer to Why does 0 factorial equal 1? for more information.
  8. Dr. Math also tells us that, depending on the context where 0^0 occurs, it can be 1, indeterminate, or undefined/nonexistent. For this game we will accept the value 0^0=1. See the Dr. Math FAQ 0 to the 0 power for more information.
  9. This site is intended for the posting of answers generated by students. Teachers may submit answers for their students.
  10. Each answer should include the expression, the name of the student, the student's grade level, and the name of the school.
  11. Use the Web form once for each answer you would like to contribute. If you send more than one solution per form submission, we will be unable to include your answers on our solution page.

The four digits can be used in any order, but we encourage you to challenge yourself to use the digits in the order 2, 0, 1, 8. We also encourage solutions using only the single digit numbers 2, 0, 1, and 8 rather than double digits like .02 or 81.

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