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?

ABC

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

One Million to Seven

One Million to Seven

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

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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.