One of the most beautiful "Local Perspective" Problems - Taiwan TST Round 3 Quiz 3 - Problem 2

TIMESTAMPS: 00:00 Intro 30 - 90 - 240 Take 15 00:24 The context of the problem 00:40 What the problem is asking 01:04 What to do when lost? Play around 01:25 Playing with n=4 and getting the LHS in general 02:50 Trying to make the numbers less than 12 04:25 What we notice with n=4 with one example 06:30 What if some 3 numbers are equal 07:20 Trying to show the sum is less than 12 13:30 Trying to see what bounds a single k_i at n=4 17:20 How does n=4 relate to the general problem 18:10 Main idea 24:00 Reflecting on the problem 24:38 Thanks for Problem Solving :)