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We received many correct solutions to this puzzle:
Elizabeth, Holly, Kelly, Harrison, Harry and Matthew from Miss Rowcliffe's Maths Class in Upton Heath C of E Primary School in Chester sent us this solution:
Numbers less than 20  5  18  15  11  1 
Numbers more than 20  30  36  45  23  25 
Odd numbers  35  21  55  7  9 
Even numbers  20  24  10  2  16 
Factors of 60  60  12  6  3  4 
Multiples
of 5

Multiples
of 3

Triangular
numbers

Prime
numbers

Square
numbers

Lydia from Woolmer Hill School sent in this solution:
Numbers lesss than 20  16  1  18  15  7 
Numbers more than 20  25  30  60  35  23 
Odd numbers  9  5  45  55  11 
Even numbers  4  12  24  20  2 
Triangular numbers  36  6  21  10  3 
Square
numbers 
Factors
of 60

Multiples
of 3

Multiples
of 5

Prime
numbers 
Vicky and Katrina, also from Woolmer Hill School, submitted this solution:
Numbers lesss than 20  4  18  6  10  11 
Triangular numbers  1  21  15  45  3 
Odd numbers  25  9  5  55  7 
Even numbers  16  12  30  20  2 
Numbers more 20  36  24  60  35  23 
Square
numbers

Multiples
of 3

Factors
of 60

Multiples
of 5

Prime
numbers

Ben, Henry, Joseph, Simon, Michael and Jake from Hampton School sent us these three different solutions.
Heidi, Lucy and Natasha from Millais School sent us this record of their work:
Initially we looked at the headings and found those that could not have any overlap,
Poppy and Hazel, also from Millais School, reported that:
We started by trial and error and got rather frustrated!