Triangular Clock
Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?
Trinni is fascinated by triangular numbers (1, 3, 6, 10, 15, 21, etc.).
She found that she could rearrange the twelve numbers on a clock face so that each adjacent pair added up to a triangular number.
She left the 12 in its usual place; what number did she put where the 6 would usually be?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Answer: 5
Triangular numbers: 1, 3, 6, 10, 15, 21, ...
Image
![Triangular Clock Triangular Clock](/sites/default/files/styles/large/public/thumbnails/content-id-5684-triangular%252520clock%252520solution.png?itok=oMRBIH1k)
Why do this problem?
This problem offers a good opportunity for students to work systematically.Possible approach
This is a good starter question to have on the board as students enter the room.Key questions
- What numbers might go next to the 12?
- How many ways of putting the numbers on the clock might there be?
Possible extension
- Can the numbers 1 - 13 be arranged in a circle so that the pairs add up to a triangle number?