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We had a few solutions sent in and here are a selection that may interest you. Although doing the activity requires a lot of thinking you may be finding it hard to focus on exactly what you are thinking with each number you decide to pick up.

Haseeb from Parkhill Junior School wrote:

I would put 1 at the first square then add 10 until it reaches the top.
Afterwards I would put 2 next to the 1 then add 10 until it reaches the top.
I would continue doing it to 3, 4, 5, 6, 7, 8, 9 and 10.

Christopher from Seoul Foreign School (SFS) 
in South Korea (Korea Republic)

The fastest way to put the numbers from 1 to 100 in one grid is by putting every number that has a zero at the end of the number in the tenth column. The grid has to start with a 1 or else if there was a zero you would have to skip out the hundred.  The zero placed numbers go in the tenth place column because of this:


The ten is in the tenth column or the tenth place.
This gets control of the pattern:

$10$, $20$, $30$, $40$, $50$, $60$, $70$, $80$, $90$, $100$

Thank you for those, and if you would approach the challenge in a different way, do let us know!