### 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?

# One Million to Seven

## One Million to Seven

Start by putting one million ($1 000 000$) into the display of your calculator.

This text is usually replaced by the Flash movie.

Can you reduce this to $7$ using just these six buttons - the $7$ key and add, subtract, multiply, divide and equals as many times as you like?

What is the shortest way can you find to do it?

### Why do this problem?

While tackling this problem, children will be applying knowledge of place value and developing a trial and improvement approach. This is an activity that looks very formidable, but, in reality, is not as difficult as it looks.

### Possible approach

It can be done on a computer using the interactivity but can be done equally well on a classroom calculator.

### Key questions

How many zeros in a million?
Which buttons are you allowed to use?
Have you tried using $77$ and $777$?
How could you keep track of what you have done?
Can you find another way of doing it?

### Possible extension

After they have found at least four ways of doing this, learners could try Two and two or even the Stage 3 problem Arrange the digits.

### Possible support

Suggest using a simple calculator and experimenting quietly to see what happens or doing this two digit activity.