Question 3: On See-through Paper
If you write the numbers
1 to 9 on a strip of see-through paper you can make it into a ring.

Then you can make a list
of the numbers that you see starting at any number on the ring. For
example, if you start on 5, your list will be:
5, 6, 7, 8, 9, 1, 2, 3, 4.
Now, take a strip of
see-through paper and divide it into eleven positions.

Going left to right, put
your list of numbers onto the strip, filling the shaded places first and
then use the last three numbers to put into positions A, B and C. For
example, with the above list, your strip would look like this and you
would have made three numbers 546, 738 and 921.

If you turn your strip
over and read the numbers in mirror writing, then you would have made the
three numbers 129, 837 and 645.
The Challenge
There are two lists of
numbers that you make from your ring which produce three numbers with the
following property:
The difference between the smallest number
and the middle number is the same as the difference between the middle
number and the largest number.
What are those lists and
do they work (i.e. have the same property) when you turn your strip over? |