Let A = 1, B = 2, . . . , Z = 26. The product of a string of letters is defined as the product of the corresponding numbers of each letter in the string. For example, the product of the four-letter string “MATH” is 13 × 1 × 20 × 8 = 2080. How many six-letter strings have a product of 32,032?
+6248 \(\text{I get the following strings} \\ \left( \begin{array}{cccccc} \text{A} & \text{B} & \text{D} & \text{G} & \text{V} & \text{Z} \\ \text{A} & \text{B} & \text{D} & \text{K} & \text{N} & \text{Z} \\ \text{A} & \text{B} & \text{D} & \text{M} & \text{N} & \text{V} \\ \text{A} & \text{B} & \text{G} & \text{H} & \text{K} & \text{Z} \\ \text{A} & \text{B} & \text{G} & \text{H} & \text{M} & \text{V} \\ \text{A} & \text{B} & \text{G} & \text{K} & \text{M} & \text{P} \\ \text{A} & \text{B} & \text{H} & \text{K} & \text{M} & \text{N} \\ \text{A} & \text{D} & \text{G} & \text{H} & \text{K} & \text{M} \\ \end{array} \right)\)
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