Changes for 2007-8 and 2008-9 have resulted in the following rules.
“Certain symbols have a default interpretation as regards grouping, as follows.
- 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.
- For the Factorial variation, ! applies to just the numeral in front of it unless the Equation-writer uses grouping symbols to indicate otherwise.
- 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.
- 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.
- 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.