GENERAL RULE: If is used for raising to a power, both base and exponent must be whole numbers. If the is used for the root operation, the index must be a counting number and the base and total value must be whole numbers.
EQUATIONS^{®}^{®} Variations Always in Effect: Elementary | ||
1. | Sideways | A cube representing a non-zero number may be used sideways in the Goal or Solution to equal the reciprocal of that number. The reciprocal is a fraction of one over the number. |
2. | Upside-Down | A cube representing a number may be used upside-down in the Goal or Solution to equal the additive inverse of that number. The additive inverse is the negative of that number. |
3. | Zero Wild | The 0 cube may represent any numeral on the cubes, but it must represent the same numeral everywhere it occurs (Goal and Solution). Each Solution-writer must specify in writing the interpretation of the 0 cube if it stands for anything other than 0 in his Solution. |
4. | Factorial | There are two occurrences of the factorial operator () available, like parentheses, to be used in the Solution and/or the Goal as the Solution-writer chooses to use them. All uses of in the Solution must be in writing. |
EQUATIONS^{®}^{®} Even Year Variations: Elementary | ||
5. | Multiple Operations | Every operation sign in Required or Permitted may be used many times in any Solution. |
6. | Smallest Prime | A means "the smallest prime bigger than A," where A is a rational number less than or equal to 200. A rational number is a whole number. |
7. | = Average | shall not represent addition; instead it shall represent the operation of averaging two numbers. |
8. | LCM | The may represent the LCM (least common multiple) of two counting numbers. |
9. | GCF | may represent the GCF (greatest common factor) of two whole numbers, provided at least one of them is not 0. |
EQUATIONS^{®}^{®} Even Year Variations: Elementary | ||
6. | Two-Digit Numerals | Two-digit numerals are allowed in solutions. |
7. | Percent | An upside down means percent of. A B means A% of B when A and B are numbers. In the Goal or a Solution A and/or B may be a two-digit numeral. |
8. | Decimal Point | The may be used as a decimal point If so used in the Goal or a Solution, an may be combined in a numeral with at most three digits. When used as a decimal, takes precedence over all other operations. This usage of does not rule out for exponentiation. Therefore, in Solutions, players are encouraged to write a decimal point instead of when they want to interpret as a decimal point. Also one may be used as a decimal point and another for exponentiation. |
9. | Number of Factors | may be used to indicate the number of counting number factors of a counting number, including the number itself and one (that is, A = the number of factors of A, where A is a counting number <= 200. |
10. | Three-Operation Solution | Any Solution must contain at least three operation symbols. The operation symbols are , , , , , and . |
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