In a certain code language, ‘FRAMED’ is coded as ‘497621’ and ‘DREAMT’ is coded as ‘769542’. What is the code for ‘T’ in that language?

Correct — D. Do not match letter to digit slot by slot — compare the two sets.

FRAMED uses the letters F, R, A, M, E, D and the digits 4, 9, 7, 6, 2, 1.
DREAMT uses the letters D, R, E, A, M, T and the digits 7, 6, 9, 5, 4, 2.

Rule: the letters common to both words must take the digits common to both codes.

Shared letters: R, A, M, E, D. Shared digits: 4, 9, 7, 6, 2.
Left over: F in the first word against 1 in the first code, and T in the second word against 5 in the second code.

So T is coded 5 — option (d).

Why the others are wrong

• (a)
  7 — 7 appears in both codes, so it is spoken for by one of the five letters both words share. It cannot belong to T, which only DREAMT has.
• (b)
  1 — 1 appears only in FRAMED's code, and the letter only FRAMED has is F. This is the code for F, not for T.
• (c)
  4 — 4 is in both codes as well, so it is taken by a shared letter. Any digit present in both strings is unavailable to T.

In this code type the digits are deliberately jumbled, so the position of a digit in the code string tells you nothing. What does carry information is membership: which letters and which digits appear in which word.

Set the two words side by side and take the intersection. Letters in both words must be coded by digits in both codes, so whatever is left over in one word must match whatever is left over in that word's code.

The method never needs the full letter-to-digit map, only the two set comparisons.

Which comparison you use depends on the letter asked for. A letter that sits in only one word takes the digit that sits in only that word's code — the case here. A letter that sits in both words takes the digit that sits in both codes.

Key facts

• The digits in this code type are jumbled, so slot position carries no information.
• The letter unique to one word takes the digit unique to that word's code.
• A letter shared by both words takes the digit shared by both codes.
• FRAMED and DREAMT share the letters R, A, M, E and D, and their codes share the digits 4, 9, 7, 6 and 2.
• F is coded 1 and T is coded 5.

Common traps

• Lining F up with 4 and R with 9 because they sit in the same place in the strings.
• Finding the shared digits and stopping, without asking which letter the leftover digit belongs to.

No directly related past PYQ was found.