A telegraphic worked example with n = 4

Here n ! + n - 1 = 24+4-1 = 27, and the base factorial bound is 3!-1, namely 5 (so keep and eye on )

• C chooses 4 numbers from 0, 1, 2, ... , 26, say: ( ) = (3, 14, 22, 23).
• A calculates ' i ' from i = 3+14+22+23 = 3+2+2+3 = 2 (mod 4); i = 2, the hidden card is , and the cards to be passed will be 3, 14 and 23 (in the order determined below:)
• A calculates ' s ' from s = 3+14+23 = 3+2+3 = 0 (mod 4); s = 0.
• After the imagined renumbering, 's new location will be 20 (= ) = 4. 5 , and so A needs to signal that ' 5 ' to P (now, though, with representation ). Since 5 = 2.2! + 1.1! then the correct (agreed) order in which to pass them is 23, followed by 14, followed by 3.
• P , on receiving the ordered triple (23, 14, 3), sees that s is 0 (23+14+3 = 3+2+3 = 0 (mod 4)).
  P knows that 's renumbered value is one of 4. 0 , 4. 1 , 4. 2 , 4. 3 , 4. 4 or 4. 5 , and, on seeing the ordered triple (23, 14, 3), reads left to right and sees that:
  
  the two numbers to the right of 23 are both smaller than it, and so
  the number to the right of 14 is smaller than it, and so
  
  Thus P knows that s = 2.2!+1.1! = 5 , knows that 's renumbered value is 4. 5 = 20, and seeing the two smaller cards 3 and 14 (smaller than the shifted value of ) knows that is not nor , and so is . P then adds 2 to 20 to obtain 22, the hidden card.