This question has been created based on the level expected at a Junior Olympiad competition or a national challenge. It can, of course, be enjoyed at any level!
Your aim is to find all the solutions (a, b), such that 13 > a > b, that solve the equation,
where N is a multiple of 13.
As is standard, a! = a.(a-1).(a-2)... 3.2.1.
Hint. Without giving away the solution, the skill here is in reducing dramatically the number of combinations of a and b so that you can focus on a quick method of enumeration. In a competition, such questions are expected to be done without even a calculator.
As always, the top prize requires a full solution and a brief method of the steps taken.
Any questions, just ask!
The Prizes
Earnings from each Brainsteem Puzzle will go towards the next Prizes.
For this Brainsteem # 4 the Prizes are:
2 SBD for the first correct answer that includes a valid method
1 SBD for one other correct answer that will be chosen randomly. That means you can still win this prize even if the answer may already be visible!
As these are maths problems, a little bit about the randomising process for the extra prizes. Every comment with a correct answer is placed in rank order using the timestamp. The probability of winning is then inversely proportional to the order in which answers are posted. It isn't that complicated! I'll write a post about it soon! For example, if only 4 people answer they are ranked 1, 2, 3 and 4. The ratios of their probabilities of winning the random prize become 12 : 6 : 4 : 3. The actual probabilities are then approximately 0.48 : 0.24 : 0.16 : 0.12. Easy! It is possible for the same person to win both prizes.
Please upvote! Resteem if you think this is a great puzzle! I will upvote all correct answers and any other interesting comments. To be fair to everyone, the prize closes after 7 days. Winners will be notified after that date and usernames posted with a solution.
Enjoy!