Introduction: Binary Number Scrabble - the Game

About: Dan Goldwater is a co-founder of Instructables. Currently he operates MonkeyLectric where he develops revolutionary bike lighting products.
ok ok, you saw Number Scrabble and you understand the merits.  but that whole decimal number thing seemed so arbitrarily based on the quantity of fingers possessed by some Roman emperor.  Daleks don't count down from ten, its just the universal translator getting in the way.  couldn't we use a system that actually makes Logical sense?  of course, you know we can.  that whole Decimal version was just for the Normals, we both know Binary Number Scrabble is the purest form of Perpendicular Intersecting Valid Tile Sequence Puzzle Game.  Well, here it is, enjoy!

Note:  Unless you are a computer engineer, embedded systems engineer, ASIC engineer or 133t h4x0r, i'd recommend playing regular number scrabble a couple times first, and then try this version.

Step 1: Make Your Tiles

To play Binary Number Scrabble, you need a game board and tiles.  As with normal number scrabble we'll just retrofit a Scrabble set with some tape and a marker.

Number/OperatorHow ManyScore value
= (equals)141
+ (add)51
- (subtract)51
× (multiply)32
÷ (divide)24
NOT (inverse)41

Step 2: The Rules

  • Except as noted, game play is similar to Scrabble (and Number Scrabble)
  • On each turn, players must make or add to a valid and correct equation.
  • Players keep 9 tiles in their hand at all times, not 7 as in normal Scrabble
  • Players form valid equations (using binary number notation) rather than words.
    • example: '1+1=10'
  • Besides the PLUS, MINUS, MULTIPLY and DIVIDE operations, you also have available the 3 basic Bitwise Logical Operations AND, OR and NOT.
    • example: '100 OR 1 = 101'
  • You can add to an existing equation on one side or both sides in a single turn.
    • example: you can add to both ends of '1+1=10' in a single turn to make '11+1=100'
  • You may only use one new '=' sign per turn
  • Order of operation:  The game will function correctly as long as you agree beforehand on the order of operation.  You can play with either "standard math" (ie, "x" preceeds "+" unrelated to the written order), or  "strict left-to-right evaluation".
    • NOT (inverse) operator applies only to the immediately following number
    • There is no implied multiplication
  • Equations can have multiple equal parts.
    • example: '10x10=100=11+1'
  • Redundant equations are valid
    • example: '1-1+1-1=0=0+0'
  • Negative numbers are prohibited unless you can agree upon your means of applying AND, OR and NOT to them. :)
  • You may not use leading '+' signs in front of a number
  • When using AND and OR on two numbers of unequal length, leading zero's are assumed on the shorter number.  Leading zeros are not assumed for NOT.
    • example:  '101 AND 1 = 1'
  • You may not use leading zeros in front of a number except when strictly required with a NOT to form a valid logic operation, in which case they must be used.
    • example: '110 = NOT 001'.
  • You may not string together arbitrary symbols
    • example: '1+xx1==10' is NOT valid.
  • In normal scrabble, you can place one word alongside another if they create a valid cross-word.  Here, a 2-character sequence can never be an equation so this generally is not possible.  As an optional rule, you may choose to allow placing alongside when only numbers are formed as the cross-words, but you still need to connect to an existing equation some other way.
  • As an optional rule, you may choose to disallow the following "Identity" equation fragments:
    • "x1"   example:  you could not turn '1+1=10' to '1+1=10x1'
    • "+0" and "-0".   example:  you could not turn '3+4=7' to '3+4=7+0'
    • optionally "AND 1" and "OR 0" as well.
    • I recommend allowing these when playing in a learning scenario, but disallowing them with experienced players as you get into tedious '1+1=10+0+0+0x1x1' situations.
  • Feel free to add XOR for Xtra fun!

Step 3: Scoring

  • Unlike Scrabble, when adding to an existing equation only the newly added tiles score points.
  • double-letter, triple-letter, double-word, triple-word squares work as usual
  • All equations earn a bonus depending on the actual numeric value of the equation.  This rewards equations of high value like '1000x11=11000' compared to ones of low value like '1+1+1+1=10'.
    • The bonus is equal to the log-base-2 of the equation value, rounded down.  In binary this is very easy, its just the largest bit.
    • The bonus is added to the equation score before applying any double and triple word scores.
    • example:  '1+1=10'.  log-base-2 is '10'.  bonus points = 2.
    • example:  '11x11=1001'.  log-base-2 is '1000'.  bonus points = 8.
  • When a player goes out, add to their score the sum of the unplayed number tiles.

Step 4: Sample Game 1

in this game we allowed the 'identity operations', you can see that at times they get a bit excessive, but its good for learning.

Step 5: Game 2

I didn't photo every single move here, but you get the idea.  Also note that about half way through we'd had really a lot of beer and we started allowing use of the 'equals' tiles rotated sideways as '11'.

Step 6: Credits

thanks to all of you who helped test this game!  i suspect you'd prefer to remain anonymous...