I Wonder... What If...?

I wonder... what if...?

When were you last curious? What was it that provoked your curiosity? What compelled you to explore further?

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Number Sandwiches 

Stage: 1, 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

More Number Sandwiches 

Stage: 3 and 4 Challenge Level: Challenge Level:1
When is it impossible to make number sandwiches?

Shogi Shapes 

Stage: 3 Challenge Level: Challenge Level:1
Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?

Robotic Rotations 

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2
How did the the rotation robot make these patterns?

Nine Colours 

Stage: 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!