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?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

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.