Required Mathematical Intelligence

Chapter 76

The businessman among the pilgrims is different from the kind of financial speculator who is "good at calculating the price of silver coins and making a fortune by ingenious exchange" and "...so intriguing and even using all his reputation as a mortgage".One morning, when the whole company was trekking, the knight, the squire, and the merchant walked side by side.They reminded him that he had not yet brought up the difficult problem of being owed to his companions.

"Really?" the businessman became excited, "I have it here. When we stop to rest later, I ask you to consider this numerical problem. We have a group of people starting this morning, and we can follow one by one. '; or one pair and one pair, called "Biyi"; or three and three, called "Pinzi"; or five and five, called "Plum Blossom"; or six and six, called "Changsan"; Or 3 by 3, called 'Mei Shi'; or a group of 5, called 'Three Five'; finally, 5 people can walk side by side. In addition, no other method can be used to make each team of riders equal Yes. Now there is a group of pilgrims who can march in formation in 6 ways, please tell me, how many people are there in total in this group of pilgrims?"

Of course, the merchant refers to the minimum number of riders that can be formed in 64 ways.

[答案：这道难题归结为：求恰好具有64个因数的最小数，这些因数包括1及其本身。这个数为7560.7560个人可以按“鱼贯”、“比翼”、“品字”共64种方法，第64种方法是7560个成为一队。商人是谨慎的，他没有提到这是在怎样的道路上走。

In order to find the number of prime factors of a given number N, we let N=apbqcr... where a, b, c are prime numbers.Then the number of factors including 1 and N itself will be equal to (p1)(q1)(rl)... Thus, in the merchant's puzzle: 7560 = 2333 x 5 x 7.]
(End of this chapter)