# Implications of New Rules for Equations

Changes for 2007-8 and 2008-9 have resulted in the following rules.

“Certain symbols have a default interpretation as regards grouping, as follows.

1. In the absence of grouping symbols, the radical sign (?) applies to just the numeral immediately behind it by default unless the Equation-writer indicates otherwise by means of symbols of grouping.
2. For the Factorial variation, ! applies to just the numeral in front of it unless the Equation-writer uses grouping symbols to indicate otherwise.
3. For the Exponent variation (Middle/Junior/Senior only), the exponent of the selected color applies to just the numeral in front of it unless grouping symbols are used.
4. For the Number of factors and (Elementary only) Smallest prime variations, x applies just to the numeral immediately behind it by default unless grouping symbols are used.
5. When the default interpretations for two symbols conflict, the expression is ambiguous, and the Equation-writer must use symbols of grouping to remove the ambiguity.

Examples

• The expression ?9! is ambiguous because the default interpretation for Factorial, which says the expression means ?(9!), conflicts with the default interpretation of ?, which specifies the interpretation as (?9)!.
• With Number of factors and Factorial, 4+x7! is ambiguous. The default interpretation for Factorial requires 4+x7! to be interpreted as 4+x(7!). However, the default for Number of Factors requires the interpretation 4+(x7)! Elementary: The same ambiguity applies to Smallest prime.
• Middle/Junior/Senior: With Number of factors and Red Exponent, 4+x122 is ambiguous. The # of factors default says the expression means 4+(x12)2 while the Exponent default says 4+x(122).
• Middle/Junior/Senior: With Factorial and Red Exponent, ?5!2 is ambiguous because the default rules clash. The ? default requires the interpretation (?5)!2. However, the ! default makes the expression ?(5!)2, which is the same meaning required by the Exponent default.

Note None of the default interpretations of symbols restricts a player’s right to interpret an ungrouped Goal as he sits fit. For example, a Goal of x4x12 with number of factors may be interpreted in two ways. If the Equation-writer wants (x4)x12, writing just x4x12 is sufficient. However, the Equation-writer may also write x(4×12) to obtain the non-default meaning.