The letters of the English Alphabet are assigned a number according to their po$-$

sition in the alphabet, eg a $=1$; e $=5$; z $=26.$ A three character string ABC is

said to be balanced if a $+$ b $=2$c$,$ eg DHF is balanced as $4+8=26.$ How many

balanced strings are there in the English alphabet? Note a letter may occur more

than once in a string.