### 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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

##### Age 7 to 11 Challenge Level:

Many of you have had an excellent stab at this problem - it requires a lot of perseverance - and you have come up with several ways, all of which take four steps. Matthew from Gayhurst School suggests:

$1 000 000 \times 7 = 7 000 000$
$7 000 000 + 777 777 = 7 777 777$
$7 777 777\div 7 777 777 = 1$
$1 \times 7 = 7$

Tom, who goes to The Oratory Preparatory School found a different way which is equally as quick:

$1000000\times77=77000000$
$+777777=77777777$
$\div 77777777=1$
$\times7 =7$

Yet another way was discovered by Robert from U-Hill Secondary and pupils from the Sutton Masterclass:

$1 000 000 \times 7 = 7 000 000$
$7 000 000 + 777 777 = 7 777 777$
$7 777 777 - 7 777 777 = 0$
$0 + 7 = 7$

Pupils from Moorfield Junior School told us about a fourth way:

$1,000,000\times 7 =7,000,000$
$7,000,000 - 7,777,777 = -777,777$
$-777,777 + 777,777 = 0$
$0 + 7 =7$

Theo, Matthew, Seth and Jessie from Christ Church Primary School went about it in this way:

$1 000 000\div 77 777 777 = 0.0128571$
$0.0128571\div 77 777 777 = 0$
$0 + 7 = 7$

This is interesting. I'm particularly intrigued by the second line. I wonder why the calculator display gives zero?

Fantastic - and to think it looked so difficult!