Digital deletions is one of the original mathematical games described by John Conway in his famous 1976 book On Numbers and Games. As always with mathematical games, playing it is only part of the fun; the best part is discovering a winning strategy.

The game is very simple:

• A series of any length of digits is written down (not all digits have to be used and a digit may be used more than once). For practical reasons, the number of digits is limited here between 6 and 18.
  
  
• On a turn, a player can:
  
  
  • change any one of the digits to a value that is less than its actual value (negative numbers are not allowed),
    
    
  • or erase a zero and all the digits to the right of it.
    
    
• The player who removes the last digit loses the game.

To the best of my knowledge, this is the first interactive JavaScript version of Digital Deletions to appear on the Web. If you know of other programmed versions, please contact me.

I am proud to announce that this page is referenced by the Drexel Math Forum.

 Number of digits:

 Strategy to use:

 Choice of digits:

Computer starts

Human starts

  Easy  

  Medium  

  Tough  

  Human  

  Computer  

• With the green LED's on the control panel you can set the number of digits you want to play with.
  
• The orange LED's allow you to choose the strategy the computer will follow:
  
  • the easy strategy is really random generated;
    
  • the medium strategy shows a partial understanding of the underlying logic, but still makes some mistakes
    
  • and the tough strategy won't give you any change, unless you are lucky and apply the winning strategy without any mistakes.
    
• The blue LED's determine the way the digits will be generated:
  
  • either defined by the human player;
    
  • or randomly generated by the computer
    
• Finally, choose the player that will have the first move:
  
  • click the human starts button to take the first move,
    
  • or the computer starts button to leave the fist move to the computer.

Click a digit to change its value. A glowing green light appears underneath the chosen digit.
If the value of this digit is

• > 0, change it with a click on one of the green leds (you can change as often as you want),
• = 0, you can only click the OK button to remove it and all the digits to its right.
  
  As long as you did not click the OK button, you can change your mind and choose another digit or another value.

After having calculated its move, the computer informs you about it with a glowing red light indicating the digit that has been changed and a panel, showing the old and the new value. Just click the digit you want to change to acknowledge the computer's move.

• You can consult a brief description of Digital Deletions.
  
  
• On Numbers and Games, the book itself, can be ordered on the Web through the well-known channels.
  
  
• A small flavour of this remarkable book can also be found on the Web.
  
  
• Or you can read a review about this book on the Web.
  
  
• You can also consult the relevant article in Wikipedia, the free encyclopaedia.
  
  
• An interesting article about surreal numbers, (the mathematical background of games) can also be found on the Web.
  
  
• The American Mathematical Society provides on its Web site an excellent introduction to mathematical games:
  
  
  • part one: the world of piles and stones
    
    
  • and part two: different moves for left and right