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In a certain code language, 'BEAM' is coded as '9483' and 'DAME' is coded as '9683'. What is the code for 'B' in the given code language?
4
8
9
3
4
Identify common letters in both words to map them to the corresponding common numbers.
Identify common letters in both words to map them to the corresponding common numbers.
Mapping the shared letters
Given BEAM = 9483 and DAME = 9683. The common letters are A, E, M. Looking at the codes, the common digits are 9, 8, 3. Thus, A, E, M correspond to 9, 8, 3 in some order.
Isolating B and D
In BEAM (9483), since {A, E, M} = {9, 8, 3}, the remaining letter B must correspond to the remaining digit 4. Similarly, in DAME (9683), the remaining letter D must correspond to the remaining digit 6.
Final Deduction
Since B maps to 4, the code for B is 4.
B: 9 is one of the digits for A, E, or M. C: 8 is one of the digits for A, E, or M. D: 6 is the code for letter D.
A is correct because the digit 4 is the only unique code remaining for B after accounting for the shared letters A, E, and M in the given words.
In coding-decoding, always list the words vertically to compare them and identify shared characters immediately; this saves time compared to manual trial-and-error.
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