Alphabet Soup

Keep sending us YOUR OWN alphanumerics and we'll publish them in collections from time to time. The following two came from Jonathan Gill, St Peter's College, Adelaide, Australia.

There is a one-to-one correspondence between digits and letters, each letter stands for a single digit and each digit is represented by a single letter. How many different solutions can you find?

Ling Xiang Ning(Allan) form Tao Nan School, Singapore, who solves many of are hardest problems, has sent 7 solutions to CARAVAN and 88 solutions to AUSTRALIAN. Is this all there are? Here is one solution to each.

Soh Yong Sheng, age 12, also from Tao Nan School, Singapore has sent this solution for.

and there are al lot more.

We have the following solutions from Allan Ling (Tao Nan School, Singapore): For the equation

T has to be 9 or 0, in order for it to satisfy T+A=A. However if T=0, it is impossible, as H+0 is not L. So T has to be 9.

The following are the possible sums (total 59):

Jonathan also proved that the following alphanumeric does not work, that is it cannot have any solutions. Well done Jonathan.

If it was an alphanumerics then H = 0 to satisfy 0 + S = S, but then H cannot be zero, otherwise C + 0 (H) = C and not R. We know that C and R cannot both represent the same number therefore

cannot be made into an alphanumeric.