Triangle numbers

There are 30 NRICH Mathematical resources connected to Triangle numbers
Summing Consecutive Numbers
problem
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Summing consecutive numbers

Age
11 to 14
Challenge level
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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Route to infinity
problem
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Route to infinity

Age
11 to 14
Challenge level
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Can you describe this route to infinity? Where will the arrows take you next?
Triangle Numbers
problem
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Triangle numbers

Age
11 to 14
Challenge level
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Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
Mystic Rose
problem
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Mystic rose

Age
14 to 16
Challenge level
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Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Handshakes
problem
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Handshakes

Age
11 to 14
Challenge level
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Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Light the Lights Again
problem
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Light the lights again

Age
7 to 11
Challenge level
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Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Iff
problem
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Iff

Age
14 to 18
Challenge level
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Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Picturing Triangular Numbers
problem
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Picturing triangular numbers

Age
11 to 14
Challenge level
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Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Take Ten Sticks
problem
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Take ten sticks

Age
11 to 16
Challenge level
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Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
Factors and Multiples Puzzle
problem
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Factors and multiples puzzle

Age
11 to 14
Challenge level
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Using your knowledge of the properties of numbers, can you fill all the squares on the board?