NOTE: {counting numbers} = {natural numbers} = {positive integers} = {1, 2, 3, 4, ...} {whole numbers} = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

GENERAL RULE: If Exponentiation is used for raising to a power, both base and exponent must be whole numbers. If the Radical 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



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.



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.


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.



There are two occurrences of the factorial operator (factorial) available, like parentheses, to be used in the Solution and/or the Goal as the Solution-writer chooses to use them. All uses of factorial in the Solution must be in writing.

EQUATIONS®® Even Year Variations: Elementary


Multiple Operations

Every operation sign in Required or Permitted may be used many times in any Solution.


Smallest Prime

Multiplication 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.


Addition = Average

Addition shall not represent addition; instead it shall represent the operation of averaging two numbers.



The Radical may represent the LCM (least common multiple) of two counting numbers.



Exponentiation 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


Two-Digit Numerals

Two-digit numerals are allowed in solutions.



An upside down Radical means percent of. A Upside Down Radical 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.


Decimal Point

The Exponentiation may be used as a decimal point If so used in the Goal or a Solution, an Exponentiation may be combined in a numeral with at most three digits. When used as a decimal, Exponentiation takes precedence over all other operations. This usage of Exponentiation does not rule out Exponentiation for exponentiation. Therefore, in Solutions, players are encouraged to write a decimal point instead of Exponentiation when they want to interpret Exponentiation as a decimal point. Also one Exponentiation may be used as a decimal point and another for exponentiation.


Number of Factors

Multiplication may be used to indicate the number of counting number factors of a counting number, including the number itself and one (that is, Multiplication A = the number of factors of A, where A is a counting number <= 200.


Three-Operation Solution

Any Solution must contain at least three operation symbols. The operation symbols are Addition, Subtraction, Multiplication, Division, Exponentiation, and Radical.

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