In a card game, each card is associated with a numerical value from 1 to 100, with each card beating less, with one exception: 1 beats 100. The player knows that 100 cards with different values lie in front of him. The dealer who knows the order of these cards can tell the player which card beats the other for any pair of cards he draws. Prove that the dealer can make one hundred such messages, so that after that the player can accurately determine the value of each card.
(In reply to
solution by Charlie)
"A>B, B>C, C>D, ... u>v, v>w, w>x, x>y, y>z
Only 99 pairs have been demonstrated, but due to the circular nature of the values (though not transitive) we know that z>A, so we have another pair to spare."
From the 99 relations given I could conclude that a possible sequence is 99>97>95>....>5>3>1>100>98>96>...>6>4>2. Specifically in this case A=99 and z=2 thus A>z rather than z>A for which your method needs.
re: solution
