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.