The subset sum puzzle

3Blue1Brown · 0m · transcribed Jul 2026

Section Insights

# 0:00

Introduction to the Game

What is the game about?

The game involves selecting 10 numbers from 1 to 100 and challenging the player to find two distinct subsets that have the same sum.

The game is based on number selection and subset sum.
The player must identify two subsets with equal sums from the chosen numbers.
The challenge is framed as a competition between the presenter and the player.

# 0:09

Understanding the Challenge

What is the specific challenge presented to the player?

The player is tasked with finding two distinct subsets from the selected numbers that add up to the same total.

The challenge requires mathematical reasoning and problem-solving skills.
An example is provided to illustrate the concept of equal sums.
The game emphasizes the importance of distinct subsets.

# 0:19

Winning Conditions

What determines the winner of the game?

The player wins if they can find two subsets with the same sum; otherwise, the presenter wins if such subsets cannot be found.

Winning depends on the player's ability to find equal-sum subsets.
The game introduces a competitive element between the player and the presenter.
The outcome hinges on the selection of numbers and the player's strategy.

# 0:29

The Puzzle's Strategy

What is the underlying puzzle of the game?

The puzzle revolves around determining which participant has the winning strategy based on the chosen numbers.

The game invites players to think critically about strategies.
It raises questions about mathematical properties of numbers.
Understanding the winning strategy is key to solving the puzzle.

# 0:38

Collaboration and Future Engagement

How can participants stay engaged with the game series?

Participants can stay subscribed to the channel or the mailing list for updates and solutions to the puzzles.

The game is part of a monthly series, encouraging ongoing participation.
Collaboration with MoMath enhances the learning experience.
Staying connected ensures access to future puzzles and solutions.

Transcript

0:00 You and I are going to play a game. The way it works is that I look at all of the numbers from one up to 100 and I choose 10 of them. I then present you with these 10 numbers and your challenge is to find two distinct subsets from whatever I choose that have the same sum. So, for example, in this case, these two different pairs of numbers each add up to 102. If you can do this, you win the game.

0:24 But, if I can find some collection of 10 numbers where no matter how hard you try, you can't find two subsets that have the same sum, then I would win the game. My puzzle for you is which one of us has the winning strategy? This is part of a monthly series of puzzlers that I'm doing in collaboration with MoMath. If you want the solution when it's out, stay subscribed either to this channel or to their mailing list.

Summary

The challenge presented involves selecting 10 numbers from 1 to 100 and determining whether two distinct subsets can be formed that have the same sum. The game hinges on the ability to find such subsets, with the outcome depending on the chosen numbers.

- The objective is to find two distinct subsets of 10 chosen numbers that yield the same sum.
- If successful, the player wins; if not, the presenter wins.
- The game explores the concept of subset sums and combinatorial number theory.
- The challenge is part of a monthly puzzler series in collaboration with MoMath.
- A solution will be provided later for those interested.
- The problem raises questions about the existence of equal-sum subsets in finite sets.