### Number Detective

Follow the clues to find the mystery number.

### Six Is the Sum

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

### (w)holy Numbers

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

# Becky's Number Plumber

##### Stage: 2 Challenge Level:

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.