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?
Age
11 to 14
Challenge level
Problem
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.
Student Solutions
Answer: 5
Triangular numbers: 1, 3, 6, 10, 15, 21, ...
Image
Teachers' Resources
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?