Patterns Triangular Numbers — Set 45
| 5 | 1 | 4 | 9 | 6 | 1 | 1 | 6 | 3 | 3 | 2 | 3 |
| 2 | 5 | 2 | 5 | 8 | 8 | 5 | 8 | 8 | 1 | 9 | 6 |
| 5 | 7 | 3 | 0 | 1 | 9 | 1 | 2 | 4 | 0 | 9 | 7 |
| 1 | 1 | 1 | 6 | 1 | 8 | 2 | 5 | 9 | 9 | 5 | 3 |
| 1 | 5 | 5 | 9 | 7 | 9 | 4 | 8 | 7 | 4 | 3 | 3 |
| 1 | 6 | 0 | 9 | 6 | 3 | 7 | 5 | 3 | 3 | 0 | 8 |
| 8 | 7 | 4 | 0 | 5 | 1 | 5 | 4 | 7 | 8 | 1 | 2 |
| 6 | 5 | 8 | 5 | 8 | 3 | 5 | 6 | 5 | 9 | 5 | 6 |
| 9 | 4 | 0 | 4 | 5 | 7 | 5 | 6 | 7 | 9 | 0 | 0 |
| 4 | 4 | 3 | 9 | 3 | 3 | 9 | 5 | 1 | 5 | 2 | 2 |
| 4 | 5 | 9 | 5 | 7 | 5 | 5 | 4 | 4 | 8 | 7 | 5 |
| 1 | 5 | 0 | 1 | 6 | 0 | 8 | 8 | 3 | 5 | 3 | 5 |
Numbers to Find
- 5154
- 0097
- 19
- 393
- 5545
- 1247
- 375
- 16
Show answer key
- : 4,6 (right)
- : 11,8 (left)
- : 9,1 (right)
- : 2,9 (right)
- : 6,8 (diagonal-down-right)
- : 6,2 (down)
- : 8,5 (down)
- : 0,5 (right)
Activity Notes
Hunt for triangular numbers in these puzzles. Triangular numbers are numbers that form equilateral triangles when arranged as dots (1, 3, 6, 10, 15, ...).
Triangular Numbers Number Search
Triangular numbers (1, 3, 6, 10, 15, 21, 28, 36, 45...) can be arranged in triangular dot patterns and equal the sum of consecutive integers. They appear in combinatorics, probability, and discrete mathematics. These puzzles build understanding of these elegant numbers through active engagement.
Triangular numbers have surprising applications in mathematics and computer science. Building fluency with these numbers develops mathematical thinking that connects to more advanced concepts in summation and combinatorial mathematics.
Tips for Finding Triangular Numbers
- Remember they increase by consecutive integers: 1, then +2=3, then +3=6, then +4=10, then +5=15, then +6=21...
- Memorize common ones: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91... These are essential references.
- Look for distinctive numbers: 55, 66, 78, and 91 are relatively distinctive and stand out in grids.
What is a triangular numbers search puzzle?
A triangular numbers search hides the sequence 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, and 91 inside a number grid. Each triangular number equals the sum of all integers from 1 up to its position.
How do I identify triangular numbers?
Triangular numbers follow the pattern n(n+1)/2. The differences between consecutive triangular numbers increase by 1 each time: +2, +3, +4, +5, and so on, forming a predictable staircase.
Where do triangular numbers appear in real life?
Triangular numbers show up in bowling pin arrangements, handshake problems, and staircase designs. Recognizing them helps students connect abstract math patterns to tangible objects.