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Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children: Mona, Bob and Jamie.
"Now", she said, "Those three numbers add to a special kind of number. What is it?"
Michael put his hand up.
"It's a square number", he answered.
"Correct", smiled Mrs Morgan.
"Oh!" exclaimed Mona, "The two numbers I can see also add to a square!"
"And me!" called out Bob, "The two numbers I can see add to a square too!"
"Oh dear", said Jamie disappointedly, "the two numbers I can see don't add to a square! It's either $5$ too little or $6$ too big!"
What numbers did the three children have on their backs?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?