Question 128
2008 boys and 2008 girls decided to get together and play the game of exchanging presents. Each participating boy was asked to bring a bouquet of flowers and each participating girl was asked to bring a bar of chocolate to the get-together. When all the participants showed up, they were lined up in some way and were seated in a circular arrangement with every one facing toward the interior of the circle. Then they were ordered to pass on simultaneously the presents they brought to the person sitting on their right in the circular arrangement. After the actions were repeated a certain number of times the situation was reached where every participating boy had in his possession a chocolate bar and every participating girl possessed a bouquet of flowers. How many possible arrangements of the chairs occupied by the boys are there?