Determine the largest integer A such that for K=1,2,3,...,length(A) the first K digits of A form an integer divisible by K.
For example, for 56165, 5 is divisible by 1, 56 is divisible by 2, 561 is divisible by 3, 5616 is divisible by 4 and 56165 is divisible by 5.
In a game of Texas Hold'em, all 5 community cards are dealt, and the three remaining players simultaneously say, "Well, there's only one hand that can beat me."
How can this situation arise? Assume that the players do not lie.
Here, "one hand" means a unique combination of 2 cards, out of the (52 choose 2) = 1326 possible ones.
For those unfamiliar with the basic rules of Texas Hold'em: each player has two face down cards, and there are five face up cards on the table. Each player makes the best possible 5-card poker hand using any of the 5 community cards and his 2 private cards.
Latest: 
Bonus: 
