14. A palindrome is a sequence of characters that reads the same forward or backward. For example, rotator, madam, Hannah, the German name Otto, and an Indian language, Malayalam, are palindromes. So are the following expressions: “Put up,” “Madam I’m Adam,” “Was it a cat I saw?” and these two sentences in Latin concerning St. Martin, Bishop of Tours: “Signa te, signa; temere me tangis et angis. Roma tibi subito motibus ibit amor.” (Respectively: Cross, cross yourself; you annoy and vex me needlessly. Through my exertions, Rome, your desire, will soon be near.) Determine the number of palindromes containing 11 characters that can be made with

(a) no letters repeating more than twice;

(b) one letter repeating three times and no other letter more than twice (the chemical term detartrated is one such palindrome);

(c) one letter repeating three times, two each repeating two times, and one repeating four times. Historical Remark: It is said that the palindrome was invented by a Greek poet named Sotades in the third Century B.C. It is also said that Sotades was drowned by order of a king of the Macedonian dynasty, the reigning Ptolemy, who found him a real bore.