Sums of Consecutive Numbers Puzzle (Tanton: Mathematics) @DrJamesTanton

Uploaded January 2011 | Updated September 2026, 3 weeks ago

7 = 3+4 and 30 = 9+10+11. Which numbers are the sum of two or more consecutive counting numbers? (For fun, try 12 and 15 and 32).

We answer this puzzle in this video using pictures of dots (though feel free to use algebra instead if you don't like pictures!) And then we can ask ... Which numbers are the sum of three or more consecutive counting numbers?

Sums of Consecutive Numbers Puzzle (Tanton: Mathematics)

Fitting Exponential Functions to Data (TANTON Mathematics)

All Quadratic Graphs are U shaped (TANTON Mathematics)

Mobius Bands / Mobius Strips (TANTON Mathematics)

What is the number e? (TANTON Mathematics)

Pigeon Hole Principle (TANTON Mathematics)

Change of Base Logarithm Rule (TANTON Mathematics)

Synthetic Division: How to understand It by not doing it. (TANTON Mathematics)