Gordon's Games - Section D (Multiplication, Division, Factors, Multiples, ...)
(original copyright,1977, by Gordon R. Scott, under the name "Two-Up".)

The Multiplying Game ( 8+ ) :

  This is played just like The Adding Game, except the possible goals are some numbers from 0 to 81, the numbers that are products of the two numbers up.
  Since it is possible to choose a goal that is not a product of any two numbers that could come up, a player may at any time, and for any reason, decide that the goal chosen is not a wise one.
  When all cards are face down, that player may then circle that written goal and write another. The circle around the number shows a loss of one point for that player.
  Goals that have been chosen, but circled, may be chosen by one other player.

Note: - The game is improved if the players first agree that the turn will not be kept when a point is made.
  - Since there are so many possible goals the players should decide first to end the game when one reaches a certain number of points, say 10.
  - For players just beginning to multiply, the upper limit of the goal set may be dropped to any reasonable point.
  - The game may be improved by taking out the 0 and/or 1 cards. This will limit the possible goals to between 4 and 81.

Example: B and C agree to end the game at 5 points, to choose from 0 to 18, and not to keep the turn when a point is made.

    B chooses to make 6, and turns up two 3's .
    C, with a goal of 12, turns up a 3 and 4 to make a goal.
    B takes the turn and finds a 6 and a 1 to make the goal of 6.
    C then takes the turn, with each having one point.

The Multiplying Game with Two or Three Cards ( 8+ ) :

  This is played exactly like The Multiplying Game except players have the option of turning up a third card after two are up.

  The range of goal choices can remain from 0 to 81, or less if desired.

Example: B has chosen 12 as a goal. B turns up a 2 and a 3.
    Since 2 times 3 is only 6, B decides to turn up a third card.
    B turns up another 2, and since 2 times 3 times 2 is 12, the goal is made.

The Dividing Game ( 7+ ) :

  This will be played just like The Adding Game but the goals chosen represent the divisors of the two figure numbers formed from the two cards up, as in The Bigger (Smaller) Number Game, Two Places.
  Goals are chosen from 2 to 9.
  The two numbers turned up are thought of as being either tens or ones, except for 0 which always takes the one's place.
  A point is made when the goal number can be divided evenly into the two figure number formed from the two face up cards.
  Once the two cards up are chosen to be a certain two figure number they cannot be switched to another as long as that player keeps the turn. That is, a player cannot make a point with 12 and right after choose 7 as a goal, pick up the 1 and 2 again, and call it 21.
  After turning up two cards the player must call out the number he/she wants them to form, if he/she thinks a goal can be made.
  If a point is made the number used to make the goal must be written beside that goal number and may not be used again by any player. That is a player with a goal of 2, finding a 1 and 2, could call them 12, but after crossing out the goal of 2 would also write 12 beside the 2. No one could use 12 again.
  The player who has made the most goals when all have been used is the winner.

Example: B has chosen a goal of 7. B turns up a 5 and 6 and calls out, "56". Since 7 divides evenly into 56, B has made one point.
  B then draws a line through the 7 and writes 56 beside it. Next B turns over the two face up cards and writes down 3 as a goal.
  Then B turns up a 5 and a 0. This can only be 50, and since it is not divisible evenly by 3, B loses the turn.
  B would be careful to see that no one else uses 56, and his opponents would watch that B didn't. All would allow 5 and 6 to become 65.

The Dividing Race ( 7+ ) :

  This is played just like The Dividing Game and The Adding Race.
  Two players start at the same end of the 2 to 9 goal set, or the opposite end.
  They may have the same goal as the other, but they will have to make it in a different way.
  The first to make all the goals, or a set number of goals, is the winner.

N.B.: Making a goal of 2 is much easier than 9. Players choosing to go opposite directions on the goal set would have to be sure they do the same goals.
  That is both doing 5 to 9 in opposite directions would be fair, but one doing 2 to 5 while the other did 9 to 6 would not be fair.

The Factors Game ( 7+ ) :   In this variation, the 0 and 1 cards are removed and the remaining cards are arranged in four rows of four.   Although the players may be dividing, the play is much like The Multiplying Game.
  Goals are chosen from 4 to 18. and are made when each of the two cards turned up divide evenly into the goal number. That is, if the goal is 16, and a 3 and 4 are turned up, since only 4 divides evenly into 16 (is a factor of 16) then a point would not be made. If 8 and 4 were turned up, a point would be made.
  As in The Multiplying Game, a player may choose a new goal before making the old one simply by circling the old one. A point is then taken from that player's total and other players are free to take the circled goal.
  For this reason players should not keep the turn after making a point.

Example: C has chosen 16 as a goal. C turns up a 2 and a 4. Both of these divide evenly into 16 so C has made a point and the turn goes to B.
  When the cards are face down, B, who has a goal of 17, decides this cannot be made. B circles the 17 and writes down 8. B then turns over the 2 and 4 to make a goal and gain back the point that was lost. The turn then goes to C.

The Multiples Game ( 8+ ) :

  This is played like The Dividing Game.
  The goals chosen are pairs of different numbers from 2 to 9.
  Points are made when each number in the goal pair will divide evenly into a two-figure number formed by the two cards up.
  The use of the two numbers turned up to form a new number is handled just as in The Dividing Game. The two figure number used to make a goal is written beside the pair and cannot be used again during the game by any player.
  Goal numbers may be used as often as possible by all players during a game, but each pair may only be used once.
  Since there are many possible pairs, the players may decide to end the game when one first reaches a certain number of points, perhaps 10.
  The turn is not kept after making a goal.

Example: B has written 2 and 5 ( 2 , 5 ) as a goal.
  B turns up a 3 and a 0 and declares this to be 30.
  Both 2 and 5 divide evenly into 30 so B has made one point.
  B turns over the 3 and 0, crosses out the 2 and 5, writes 30 beside them, and writes 2 and 6 as a new goal pair. The turn then goes to C.

Fraction and Decimal Games ( 8+ ) :

  Playing The Bigger (or Smaller) Number Game, Two Places, could benefit children with some understanding of fractions and / or decimals.

  To simulate fractions, one card could be placed over the other to form a numerator and denominator.   The smaller number would always go on top (unless they were the same).
  (You might have a reason for eliminating this last rule.)
  It could be a real challenge to decide which player had formed the bigger, or smaller, fraction.

Example: B turns up a 2 and a 5. B arranges them as 2/5.
  C turns over a 3 and a 4. C arranges them as 3/4.
  Who wins a point? Which fraction goes in the garbage pile.

  To simulate decimals, each player could have a supply of buttons to use as the decimal point.
  Players would then not only have to consider where to place each number up, but would have to think of where to place the decimal point.
  A useful rule could be that the decimal point always went between the numbers or before the numbers, never after.

Example: B turns over a 2 and a 5 and is trying to make the smaller number.
  B can choose from .25, .52, 2.5, 5.2.
  C turns over a 3 and a 4. C can choose to make .34, .43, 3.4, 4.3.
  B, with the right choice, will be the winner.

  The Adding to Fifty Game and The Adding to Fifty Race could be modified to use fractions (very difficult) or decimals. Rules would have to set a small goal, say 5.
  (The sum of all the whole numbers in the 20 card set is 90.)

  This is the end of the number games using the simple 0 to 9 cards.
  The reader is, as stated before, free to change the rules, and free to adapt the games to new uses.
  If you discover a new game, please let me know what it is if you wish it to be considered for inclusion in this set.
  I'm sure I've thought of other games, but I can't find where I put them.