# The 10,958 Problem - Numberphile | Summary and Q&A

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April 18, 2017
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Numberphile
The 10,958 Problem - Numberphile

## TL;DR

A mathematician finds an interesting number trick and showcases cheat sheets that can represent any three-digit number using a single digit, but he stumbles upon a missing number in his list.

## Key Insights

• #️⃣ The number trick demonstrated in the video allows any three-digit number to be written as an expression using a single chosen digit and specific operations.
• 🚰 Cheat sheets created by a mathematician from Brazil provide comprehensive tables and formulas to represent three-digit numbers using any chosen digit.
• 📼 The video highlights the existence of the 10,958 problem, where the number 10,958 is missing in its ascending representation using a specific set of operations.

## Transcript

I think I have a solution to a... very much an unkown problem, it's a, this is a problem no one was really looking for a solution for, but I think I found one. So there's a thing called the 10958 problem. To demonstrate what the problem is, I'm gonna start with a little number trick a little something, a little bit of number showmanship. Like all g... Read More

## Questions & Answers

### Q: How does the number trick work?

The number trick involves taking a three-digit number and writing it as an expression using only the chosen single digit, along with specific operations. This is achieved by manipulating the digits and using exponents and addition.

### Q: What are the cheat sheets shown in the video?

The cheat sheets created by the Brazilian mathematician contain tables and formulas that allow individuals to represent any three-digit number using any single digit chosen. These cheat sheets provide a comprehensive guide for writing out numbers using specific operations.

### Q: Is there evidence to support that the cheat sheets provide the shortest representations?

The video does not provide explicit evidence to support that the cheat sheets offer the shortest representations. The mathematician claims that these are the minimal possible digits, but it is unclear how this has been verified or if other solutions exist.

### Q: What is the 10,958 problem?

The 10,958 problem refers to the missing representation of the number 10,958 in ascending order using a specific set of mathematical operations. This number is the only gap found in the ascending representations of numbers up to 11,111 and remains unsolved.

## Summary & Key Takeaways

• The video introduces the 10958 problem, a mathematical conundrum involving the missing representation of the number 10,958 in ascending order using a specific set of operations.

• The mathematician demonstrates a number trick where any three-digit number can be written as an expression using a single digit chosen by the participant.

• Cheat sheets created by a mathematician from Brazil are showcased, providing tables and formulas to represent three-digit numbers using any single digit.

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