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Free Addition Arithmagon Generator – Printable Number Triangle Puzzles

Create printable arithmagon worksheets in seconds. Choose “operands given”, “sums given”, or mixed difficulty and download ready-to-use PDFs for your math lessons.

CREATE YOUR ARITHMAGON PUZZLE

An arithmagon, also known as a number triangle puzzle, is a math puzzle where the numbers on the sides are created by adding the corner numbers.

Create printable addition arithmagon puzzles

Include solution page
Paper format:

What are Addition Arithmagons?

An addition arithmagon is a triangle puzzle with operands at its vertices and their sums written on the edges between them. There are three types of puzzle:

  • Operands given. The easiest type. The numbers at the vertices are shown — add any two to find the sum on the connecting edge.
  • Sums given. The most challenging type. The sums on the edges are given and you must work backwards to find the operands at the vertices.
  • Mixed. A middle-ground challenge: two sums on the edges and one operand at a vertex are revealed. Find the rest.

How to Solve an Arithmagon Puzzle

The Arithmagon

A triangle with operands on the corners and sums on the sides.

a b c ab ca bc

1. All Sums Given

Given: ab, bc, ca
Find: a, b, c

  1. Add all three sums.
  2. Divide by 2 to get total of a + b + c.
  3. Find each value:
a = ab+ca-bc 2 b = ab+bc-ca 2 c = bc+ca-ab 2

2. All Operands Given

Given: a, b, c
Find: ab, bc, ca

  1. Add adjacent operands.
  2. Repeat for all sides.
ab=a+b bc=b+c ca=c+a

3. Mixed Information

Given: Some values

  1. missing = sum - known
  2. Fill values step-by-step.
  3. Use completed sides to solve others.
  4. Check consistency.

How to Use Arithmagons in the Classroom

Use as a warm-up: Start your lesson with a quick arithmagon to activate mental math skills. “Operands given” works best for fast starters.

Differentiate difficulty:

  • Operands given: You add the corner numbers to find the edge values.
  • Sums given: You work backwards from the edge values to find the corner numbers.

Choose the right level:

  • Beginners: Operands given
  • Intermediate: Mixed
  • Advanced: Sums given

Encourage problem-solving: Ask students to explain their steps, especially for “Sums given” puzzles where reasoning matters more than calculation.

Use for independent or group work: Students can solve individually, compare answers in pairs, or explain strategies to the class.

Provide immediate feedback: You can include a solution page in the worksheet to allow quick checking and self-correction.

More Arithmagon & Addition Puzzles

  • Multiplication Arithmagon Maker
    The same triangle puzzle format using multiplication instead of addition.
  • Addition Maze
    Navigate a printable maze by solving addition problems along the correct path.
  • Open The Safe
    Crack the combination by solving a chain of addition calculations.
  • Addition Wheels
    Fill in the spokes of a number wheel by adding the hub number to each rim number.

FAQ for Number Triangle Puzzles

What is the difference between operands given and sums given?

 Operands given means you add the corner numbers to find the edge values. Sums given means you work backwards from the edge values to find the corner numbers.

Which arithmagon puzzle type is best for beginners?

 Operands given is the easiest. Mixed is intermediate. Sums given is the most challenging.