Final answer:
To find the number of length 13 palindrome strings from the set {a, b, c, d}, we calculate 4^6, which is 4096, since only the first half of the string determines the entire palindrome.
Step-by-step explanation:
The student's question pertains to the number of palindrome strings of length 13 that can be formed from the set {a, b, c, d}. A palindrome is a sequence that reads the same forwards and backwards. Considering a palindrome of length 13, the middle character can be any of the four characters from the set since it does not affect the symmetry. The remaining 12 positions will be split into two halves, each mirroring the other. Therefore, we only need to choose 6 characters for the first half because the second half is determined by the first half to maintain the palindrome property.
We have 4 choices for each of the 6 positions in the first half, resulting in 4^6 possible combinations. This leads to 4096 unique palindromic strings of length 13. We do not need to consider the middle character separately in this calculation since its choice is independent and included in the 4^6 combinations.