Can someone further explain the reason why we isolate the remaining of two employees to get the answer of 100k? (this is from quant section #1’s video explanation)

A company has a “bonus pool” it distributes to its 12 employees at the end of the year. This year’s “bonus pool” is $300,000 and each employee is to receive at least $10,000. If one of the employees wants to ensure that he or she has the largest bonus of the 12 employees, his or her bonus must be greater than what amount?z

The question has a tricky wording. But what we are trying to calculate is from the perspective of the employee who wants to be sure she/he got the biggest bonus. He wants to be able to look at his amount and know this is the highest. For that you need a bonus high enough that none of the other employees could possibly get the same amount. The question demands the lowest such number for which the an employee will know their bonus is the highest.

Now if you look at the answer, if one employee gets 100k, you have to divide the remaining 200k amongst 11 employees with the condition each gets at least 10k. Now let’s say another employee got the same amount, 100k as well. The remaining 10 employee will get the minimum amount in this scenario and this exactly is your edge case. Any bonus above 100k would mean that no other employee was able to receive the same amount because of the 10k minimum condition.