In a certain code language, ‘WACK’ is coded as ‘3589’ and ‘CAKE’ is coded as ‘5138’. What is the code for ‘E’ in the given code language?
1
Each letter gets one digit, so letters common to both words must take the digits common to both codes (the order of digits is jumbled).
WACK and CAKE share the letters A, C and K. The codes 3589 and 5138 share the digits 3, 5 and 8. So {A, C, K} ↔ {3, 5, 8}.
In WACK the extra letter W must take the extra digit 9, and in CAKE the extra letter E must take the extra digit 1. Therefore E is coded as 1.
Check: removing the common digits 3, 5, 8 from 5138 leaves only 1, and removing the common letters A, C, K from CAKE leaves only E, so the code for E is 1.
Hence, 1.
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