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Illuminations: Sum of Threes

The number 4 can be expressed as the sum of three positive integers in only one way:

4 = 1 + 1 + 2

However, the number 50 can be expressed as the sum of three positive integers in 200 ways.

Somewhere in between, there is a number n that can be expressed as the sum of three positive integers in precisely n ways. Can you find n?

This brainteaser was written by Derrick Niederman.


Math Topics
Addition & Subtraction, Algebra & Pre-Algebra
Middle School, High School
7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade
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Problem and solution

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Organization

National Council of Teachers of Mathematics

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Type of Resource

Activity Sheet
PDF File

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Resource k12

Illuminations: Sum of Threes

The number 4 can be expressed as the sum of three positive integers in only one way:

4 = 1 + 1 + 2

However, the number 50 can be expressed as the sum of three positive integers in 200 ways.

Somewhere in between, there is a number n that can be expressed as the sum of three positive integers in precisely n ways. Can you find n?

This brainteaser was written by Derrick Niederman.


Math Topics
Addition & Subtraction, Algebra & Pre-Algebra
Middle School, High School
7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Descriptions of PDFs

Problem and solution

What are you looking for?

Organization

National Council of Teachers of Mathematics

Website URL

Type of Resource

Activity Sheet
PDF File

Assigned Categories