In a certain code language, ‘LAMP’ is coded as ‘6829’ and ‘LAME’ is coded as…

Concept: in this kind of letter-to-number coding the digits are not tied to the positions of the letters. A code is simply a jumbled collection of digits, one digit standing for each letter of the word. Two such words can therefore be compared as collections: a digit lying in both codes must stand for a letter lying in both words, while a digit lying in one code alone must stand for the letter that only that word contains.

Application: place the two given words next to their codes.

Now work through the comparison step by step.

1. LAMP and LAME begin with the same three letters L, A and M, and differ only in their last letter — P in LAMP and E in LAME.

2. Write each code as a collection of digits: 6829 gives 2, 6, 8 and 9, while 2619 gives 1, 2, 6 and 9.

3. The digits lying in both collections are 2, 6 and 9 — three shared digits for exactly three shared letters, so 2, 6 and 9 stand for L, A and M in some order.

4. That leaves 8 in the code of LAMP, and P is the letter of LAMP still without a digit, so P = 8.

5. That leaves 1 in the code of LAME, and E is the letter of LAME still without a digit, so E = 1.

Cross-check: rebuild both codes from this assignment. L, A and M take 2, 6 and 9 in some order; adding P = 8 gives exactly the four digits of 6829, and adding E = 1 gives exactly the four digits of 2619. Both codes are reproduced, so the code for E is 1.

Note: the data do not separate L, A and M from one another, and they need not — the question asks only for the digit standing for E.