Use the digits in the year 2012 and the operations
+, -, x, ÷, sqrt (square root),
^ (raise to a power), and ! (factorial),
along with grouping symbols, to write
expressions for the counting numbers 1 through 100.
- All four digits must be used in the expression.
- Only the digits 2, 0, 1, 2 may be used.
- Multi-digit numbers such as 20, 210, or .02 MAY
be used this year. Note that 0.02, while equivalent to .02, would not be acceptable since only one 0 is available this year.
- 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 + 2)^2 - 0! is an acceptable way to write 8, because ^ is an acceptable operation and it uses exactly the digits 1, 2, 2, and 0. But 2^2 + 2 + 1 + 0! is not acceptable, because "^2" is not an acceptable operation, and there are not three 2's available. Similarly, 2^3 + 2 - 1 - 0! would not be acceptable since "^3" is not an acceptable operation.
The Knollwood School 7th grade (from Fair Haven, NJ) wrote to ask if double factorials (!!) can be used. I'd never heard of double factorials, and was impressed that they had researched the operation, so I'm allowing them. Not sure what one is? Check out what Dr. Math has to say about them here: http://mathforum.org/library/drmath/view/56085.html
By popular demand, multifactorials may also be used this year. Thanks to everyone who wrote to teach me about them! (or should I have used more exclamation points there?)
- The integer function may NOT be used. Nor may the round, floor, ceiling, or truncate functions.
- Students should be introduced to the fact that 0! by definition
is equal to 1. See Dr. Math's answer to Why
does 0
factorial equal 1? for more information.
-
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.
- This site is intended for the posting of answers generated by
students. Teachers may submit answers for their students.
- Each answer should include the expression, the name of the
student, the student's grade level, and the name of the school.
- 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 will be more likely to publish expressions with the digits in the order 2, 0, 1, 2.
Return to 2012 Mathematics Game and
submission form.
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