Can you solve these counting problems?

Описание: There are 100 players in a single elimination tournament. How many matches need to be played? Three sets have their union as the integers from 1 to 10, and their intersection is the empty set. How many such sets are possible? Special thanks this month to: Mike Robertson, Daniel Lewis, Kyle, Lee Redden. Thanks to all supporters on Patreon!   / mindyourdecisions  

0:00 problems
2:25 solution 1
5:18 solution 2

Problem 1
The College Panda
https://thecollegepanda.com/12-tricky...
Brainly
https://brainly.com/question/13082487
AoPS 2023 AMC 10B, P15
https://artofproblemsolving.com/wiki/...
Problem 2
1985 Putnam A1
https://prase.cz/kalva/putnam/psoln/p...
Twitter
  / 1  
1985 Putnam
https://kskedlaya.org/putnam-archive/...
Math StackExchange
https://math.stackexchange.com/questi...
1985 Putnam solutions
https://math.berkeley.edu/~giventh/19...

More Putnam videos
--------------------------------------
1968 Putnam exam A1
An integral that implies pi is less than 22/7
   • Legendary test question - π is less than 22/7  

2004 Putnam A1
If your free throw percentage is below 75%, and later is above 75%, is there necessarily a point where it is exactly 75%?
   • The hardest test had this "easy" question ...  

1978 Putnam B1
A convex octagon inscribed in a circle has four consecutive sides of length 3 and four consecutive sides of length 2. Find the area of the octagon.
   • The smartest students solved this by think...  

1994 Putnam A2
Finding the area of a sector of an ellipse
   • Secret math trick to solve a Putnam questi...  

1989 Putnam A4
For an irrational number &alpha between 0 and 1, is there a finite game with an unbiased coin such that the probability of one player winning the game is α?
   • Problem From The Hardest Test - Use A Coin...  

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