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## 'Becky's Number Plumber' printed from http://nrich.maths.org/

Thank you to all those of you who submitted
solutions to Becky's Number Plumber problem.

Joshua sent us a particulary well-explained
solution:

If there is an even number in the feedback box the answer's unit
digit will always be $6$.

If you put an odd number in the feedback box the answer's unit
digit will always be $1$.

When we multiply $5$ by an even number the answer will always be a
multiple of ten, so when we minus $4$ from this number the final
answer's unit digit will be $6$.

If you multiply $5$ by an odd number the answer's unit digit will
always be $5$ and then if you minus $4$ from this number the unit
digit of the final answer will be $1$.

Matthew and Hannah from Stanbridge point out
that:

The rule doesn't work if you put in $0$. The answer is $-4$.

Well done too to the following who sent in
clear solutions:

Velina, Ben, Emily, Max, Alex, Matthew, Lucy,
Paige and Ross from Ickford Combined School

Jasper, George, James and Ed from St Peter's
College

Maya, Marlee, Ethan, Joshua, Samara and Taylor
from Sylvan Park.

I wonder whether anyone found any numbers that
work in a similar way? Do let us know if you've
discovered something interesting.