| Additional minute | The extra 60 seconds a player receives to complete what he must do after the first time limit has expired; by the end of this extra minute, the player must complete the action or receive a second -1 and forfeit what he is doing |
| Advanced On-Sets | The form of On-Sets in which Restrictions are used; Middle, Junior, and Senior Divisions play Advanced On-Sets |
| Adventurous On-Sets | The form of On-Sets in which players choose variations at the beginning of each shake; all four divisions play this form of the game |
| Adventurous variation | One of a list of special rules used in On-Sets; for each shake each player must select one or two rules from the list for the appropriate division |
| Ambiguous Goal | A Goal that has more than one legal interpretation; this can happen only when the Absolute value variation is in effect in Middle, Junior, or Senior division |
| Ambiguous Solution | A Solution that has more than one legal interpretation |
| Basic On-Sets | The form of On-Sets in which neither Restrictions nor adventurous variations are used |
| Blank card | The On-Sets card that has no color dots on it |
| “Bonus” | The word a Mover must say before making a bonus move |
| Bonus move | A move to Forbidden which a player makes after saying the word “Bonus” and before making another move to any one of the three sections of the mat |
| Chain Restriction | An On-Sets Restriction that contains two or more = or C symbols |
| Challenge | A claim by an opponent that a Solution is possible Now or that it is Never possible |
| Challenge block | An object that a Challenger must pick up in order to challenge |
| Challenger | The player who makes a legal challenge |
| Clockwise | To the left |
| Color cube | A cube with a color dot on each of its faces |
| Complement of a set | The set of cards in the Universe that not in the set; this operation is indicated by the symbol ‘ |
| Correct Solution | A Solution that satisfies all the requirements listed in Section VII-B of the On-Sets Tournament Rules |
| Cube | A block containing a symbol on each of its six faces |
| Deal cards | Shuffling the cards, then setting out of the required number of cards from the top of the face-down deck in the dealer’s hand (that is, the dealer may not select which cards to deal) |
| Digit | One of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Digit cube | A cube containing the digit 1 on two of its faces and the digits 2, 3, 4, and 5 on the other four faces |
| Division | One of the four levels of competition: Elementary (grade 6 and below), Middle (grade 8 and below), Junior (grade 10 and below), and Senior (grade 12 and below) |
| Elementary Division | The division of play for students in grade 6 and below |
| Empty set | The set consisting of no cards |
| Forbidden | The section of the playing mat labeled FORBIDDEN; cubes in this section may not be used in any Solution |
| Forceout | The term used for the situation in which the last cube from Resources is played to Required or Permitted |
| Goal | The physical configuration of one or more digit cubes placed on the GOAL section of the playing mat; also any number represented by a legal interpretation of those cubes |
| “Goal” | The word the Goal-setter says when finished setting the Goal |
| Goal section | The section of the playing mat where the Goal is placed |
| Goal-setter | The player who rolls the cubes and sets the Goal |
| Grouping symbols | Symbols used in pairs (such as parentheses, brackets, and braces) to indicate the order of operations in a Solution |
| Illegal challenge | After a player picks up the challenge block, (a) a claim other than Now or Never or a No Goal challenge, (b) a Now or Never claim by the last Mover (who is therefore challenging himself), (c) a Now or Never claim before the Goal has been completed, (d) a Now claim with no cubes in Required or Permitted, (e) a Now claim with fewer than two cubes left in Resources, or (f) a Never claim after the first minute following the move of the last cube in Resources to Required or Permitted |
| Illegal procedure | A move or other action that violates a procedural rule; examples: moving out of turn, attempting to make a bonus move without first saying “Bonus” |
| Illegal Universe | A Universe consisting of too many or too few cards; in Elementary, Middle, and Junior Divisions, the Universe must contain from 6 to 10 cards; in Senior Division, the Universe must contain from 10 to 14 cards |
| Incorrect Solution | A Solution that violates one or more stipulations of section VIIB of the On-Sets Tournament Rules |
| Insulation | The process whereby an illegal procedure is protected from correction by a subsequent legal action by another player |
| Intersection | The operation represented by the symbol Ω; the intersection of two sets is the set consisting of the cards contained in both sets |
| Invalid challenge | Same as Illegal challenge |
| Junior Division | The division of play for students in grade 10 and below |
| Legal interpretation | An evaluation of the Solution or the Goal that does not violate the rules of mathematics or the game of On-Sets |
| Legal move | (a) A bonus move by the Goal-setter (who is not leading in the match), (b) setting a legal Goal by the Goal-setter, or (c), after the Goal has been set, the transfer of a cube from Resources to Required, Permitted, or Forbidden by the player whose turn it is with the exception that the last cube in Resources may not be legally played to Forbidden |
| Match | A sequence of shakes played continuously by two or three players until a specified time limit has been reached |
| Middle Division | The division of play for students in grade 8 and below |
| Minus | A word used for the operation of set subtraction (–) |
| Minute | The length of time it takes all the sand to pass from the top half of the timer to the bottom half |
| Move | The setting of the Goal or the transfer of a cube from the Resources to Required, Permitted, or Forbidden |
| Mover | The player who made the most recent move |
| Negative number | A number smaller than 0 |
| “Never” | The word a player says when making a Never Challenge |
| Never Challenge | A challenge that no correct Solution can be written using all the cubes in Required, none, some, or all the cubes in Permitted, and none, some, or all the cubes in Resources |
| “No Goal” | The words the Goal-setter must use to make a no Goal declaration |
| No Goal challenge | The claim by an opponent that the no Goal declaration of the Goal-setter is incorrect; section III-D of the On-Sets Tournament Rules explains how to work out this challenge |
| No Goal declaration | The claim by the Goal-setter that no Goal can be set which has a possible Solution from the remaining Resources |
| “Now” | The word a player says when making a Now Challenge |
| Now Challenge | A challenge that a Solution can be written using all the cubes in Required, none, some, or all the cubes in Permitted, and, if needed, one cube in Resources |
| Null set | Same as empty set |
| Numeral cube | Same as digit cube |
| Operation cube | A cube with an operation symbol on every face |
| Operation symbol | One of the symbols U, Ω, –, or ‘; this definition applies whether these symbols have their usual mathematical meanings or special meanings defined by variations |
| Order of operations | The sequence in which operations are to be performed in the Goal or a Solution |
| Penalty | The punishment a player receives for an illegal action; examples: loss of one point, returning an illegally played cube to Resources |
| Permitted | The section of the playing mat labeled PERMITTED; cubes in this section may be used in any Solution |
| Playing mat | The rectangular piece of cardboard (or, in older games, two rectangular cardboards) that contains the REQUIRED, PERMITTED, FORBIDDEN, and GOAL sections; even if the physical mat contains a RESOURCES section, this is not considered part of the playing mat |
| Regular move | A move that is not a bonus move; that is, play of a cube from Resources to the mat without calling “Bonus” or the second move on a turn after a bonus move |
| Required | The section of the playing mat labeled REQUIRED; cubes in this section must be used in any Solution |
| Resource cube | A cube that has been rolled for the shake but has not yet been played to the Goal, Required, Permitted, or Forbidden sections |
| Resources | The symbols that appear on the top faces of the cubes after they have been rolled for the shake |
| Restricted Universe | The Advanced On-Sets Universe after the Restriction part of a Solution has been applied to the original Universe |
| Restriction | In Advanced On-Sets, a statement containing one or more = or C symbols |
| Restriction cube | A cube containing the symbols =, C, V, and /\ on its faces |
| Restriction part | That part of an Advanced On-Sets Solution consisting of one or more Restrictions |
| Restriction statement | Same as Restriction |
| Round | Same as Match | |
| Scoresheet | A piece of paper on which players’ scores for the shakes of a match are recorded and totaled and which the players sign or initial and which the winner of the match (or one of the winners if there is a tie) turns in to a designated person or place when the match ends | |
| Senior Division | The division of play for students in grade 12 and below | |
| Set-Name | An expression which names a set of zero or more cards from the Universe | |
| Set-Name part | That part of a Solution which consists of one Set-Name | |
| Set Subtraction | The operation represented by the symbol –; Set1 – Set2 produces the cards that are in Set1 but not in Set2 | |
| Shake | A play of the game starting with the roll of the cubes and a deal of the cards and ending with at least one player writing a Solution | |
| Solution | A Set-Name part and, if necessary in Advanced On-Sets, a Restriction part | |
| Solution-writer | A player who must present a Solution after a challenge or after the last Resource cube is moved to the playing mat | |
| Subtraction | Same as Set subtraction | |
| Symbols of grouping | Same as grouping symbols | |
| Symmetric difference | The operation defined by the Symmetric difference variation for the symbol –; Set1 – Set2 produces the cards that are in either Set1 or Set2 but not in both | |
| Table | A group of two or three players competing against each other in a match | |
| Ten-second warning | The countdown from 10 to 1 that an opponent must make out loud when the sand runs out on a player’s time limit | |
| Third Party | In a three-player match in which a challenge has been made, the player who is neither the Challenger nor the Mover | |
| Timed player | A player who is being timed to complete a task (roll the cubes, set a Goal, make a move, write or check a Solution, etc.) | |
| Time limit | The amount of time allotted by the rules for a player to complete an action | |
| Timer | An hour-glass-shaped piece of plastic (or glass) containing sand that is used to determine one- and two-minute time limits during a match; the sand in a timer usually takes about 60 seconds to pass through | |
| Turn | The time when a player is obligated to move (which includes setting the Goal), challenge, or complete a required action (e.g., selecting a variation) within some specified time limit | |
| Union | The operation represented by the symbol U; the union of two sets is the set of cards that are in either set or both | |
| Universal set | The set of all cards dealt for a shake | |
| Universe | Same as Universal set | |
| Universe chart | A chart consisting of squares in which the cards in the Universe can be recorded | |
| Valid challenge | A challenge that is not illegal | |
| Variation | Same as Adventurous variation | |
| Variation selection | A player’s choice of one or two variations from the appropriate list; the player indicates the selection by circling the name of the variation(s) on the variation selection chart and, if necessary, filling in the blank to indicate which cube is wild or required, etc. | |
| Warning | The announcement that the time limit for the match (round) has been reached and that no new shakes are to be started |
| Wild cube | A cube containing a symbol on its top face which may represent another symbol because of a variation chosen for the shake |
Variation selection chart A chart printed either on the back of the scoresheet or on a separate page on which each player must record his/her variation selection for each shake on this chart
