### Digit Sum

What is the sum of all the digits in all the integers from one to one million?

### Legs Eleven

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

### Football Sum

Find the values of the nine letters in the sum: FOOT + BALL = GAME

##### Age 11 to 14 Challenge Level:

The number $747$ can be formed by adding a $3$-digit number
with its reversal: $621 + 126 = 747$, for example.

Can you find the other two ways of making $747$ in this way?

Which other numbers between $700$ and $800$ can be formed from a number plus its reversal?
There are more than five...

Can you explain how you know you have found all the possible numbers?

How many numbers between $300$ and $400$ can be formed from a number plus its reversal. And between $800$ and $900?$...

The number $1251$ can be formed by adding a $3$-digit number with its reversal.
Which other numbers between $1200$ and $1300$ can be formed from a number plus its reversal? And between $1900$ and $2000?$...

With thanks to Don Steward, whose ideas formed the basis of this problem.