Tricks With Big Numbers

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Extracting Characters From Keywords Tricks With Big Numbers So Where Are We Now?

Now that we have the string representation of all the digits and the letter 'e', we can use JavaScript’s exponent notation to construct strings that represent large numbers such as 10100 and 101000:

  • Form the strings '1e100' and '1e1000'
  • Coercing these strings to numbers gives 1e+100 and Infinity
  • Coercing these numbers back to strings to give '1e+100' and 'Infinity'
  • Extract the characters '+', 'I' and 'y'

Plus Sign

It might seem almost magical that the '+' sign can be obtained from a string containing only the characters 1e100; however, when this string is coerced to a number then back to a string, JavaScript helpfully inserts the '+' for us…

  +'1e100'          // Create the string and coerce to a number -> 1e+100
 (+'1e100')+[]      // Overload plus to convert the number back to a string -> '1e+100'
((+'1e100')+[])[2]  // Extract the character at index 2 -> '+'

Here’s the above code with 'e', 1 and 0 represented in their encoded form:

 +(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[]))                 // Coerce string '1e100' to number 1e+100
 +(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[]))+[]              // Coerce back to string '1e+100'
(+(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[]))+[])[!![]+!![]]  // Extract character at index 2 -> '+'

Two More Alphabetic Characters

The number 1e+1000 is too large for JavaScript to store as a 64-bit floating point number, so instead, it simply returns the keyword Infinity. This is very helpful because it contains the previously unavailable characters 'I' and 'y'

 +(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[])+(+[]))           // Number Infinity
 +(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[])+(+[]))+[]        // Coerce to string 'Infinity'
(+(+!![]+(!![]+[])[+!![]+!![]+!![]]+(+!![])+(+[])+(+[])+(+[]))+[])[+[]]  // Extract character at index 0 -> 'I'
                                                                         // Extract character at index 7 -> 'y'