Solution

155498

First name
Maths club
School
St Peters Catholic Primary school
Country
Age
10
Email address
claire.farley-hills@st-peters-sittingbourne.kent.sch.uk

It's is easy to make all the differences odd - by using consecutive numbers forwards and backwards . We need to have at least one odd number in each row or column.
We could not find a solution where all the differences were even, we think you would need one more odd or even number to fullfill that criteria, or if we could use one of the numbers twice.