In a certain code language, the word TOAST is written as 56345 and the word TRAIN is written as 59310. Using the same letter to digit code, how is the word TORN written in that language?

Introduction / Context:
This coding question uses a substitution from letters to digits. We are told how two words, TOAST and TRAIN, are represented numerically, and we need to deduce the underlying letter to digit mapping. Once we determine which digit corresponds to each letter, we can code the new word TORN. These problems encourage systematic mapping and cross checking between the given examples.

Given Data / Assumptions:

• TOAST is written as 56345.
• TRAIN is written as 59310.
• We must code TORN using the same mapping.
• The mapping from letter to digit is one to one: each letter has a unique digit and vice versa, within the scope of the words used.
• All letters are uppercase and digits are from 0 to 9.

Concept / Approach:
We write the letter digits pairs from both coded words and match them by position. In TOAST, the letters T, O, A, S, T correspond to digits 5, 6, 3, 4, 5. This immediately tells us that T maps to 5, O to 6, A to 3, and S to 4. In TRAIN, the letters T, R, A, I, N correspond to 5, 9, 3, 1, 0, giving us mappings R to 9, I to 1, and N to 0. Combining these, we obtain a full mapping for all letters that appear in the problem, which we can then use to encode TORN.

Step-by-Step Solution:
Step 1: From TOAST → 56345, record the mappings T → 5, O → 6, A → 3, and S → 4.Step 2: From TRAIN → 59310, record T → 5 (confirming the previous mapping), R → 9, A → 3 (also confirming), I → 1, and N → 0.Step 3: Summarise the mapping: T is 5, O is 6, R is 9, N is 0, A is 3, S is 4, and I is 1.Step 4: For the word TORN, list the letters in order: T, O, R, N.Step 5: Substitute each letter with its digit: T → 5, O → 6, R → 9, and N → 0.Step 6: Combine the digits to get the code 5690.

Verification / Alternative check:
We can verify by rechecking that the mapping indeed produces the original codes. Using T → 5, O → 6, A → 3, S → 4 we recover 56345 for TOAST. Similarly, T, R, A, I, N become 5, 9, 3, 1, 0, giving TRAIN as 59310. Since both examples are consistent with our mapping and no contradictions arise, the mapping is sound and its application to TORN is trustworthy.

Why Other Options Are Wrong:
The option 5634 uses the digits for T, O, and S, but S is not part of the word TORN, so it cannot be correct. The code 5609 uses digits that do not match the letter sequence TORN under the derived mapping because R and N must correspond to 9 and 0 instead. The code 5663 again introduces A or S type digits in the wrong positions. The distractor 5990 repeats the digit 9 for both O and R, which is inconsistent with the mapping derived from the examples. Only 5690 preserves the correct letter to digit mapping in the correct order.

Common Pitfalls:
Sometimes candidates misalign positions and assume that each word must use a new mapping, which is not allowed here. Another typical error is to forget that the same letter must always correspond to the same digit, leading to inconsistent assignments. Writing the mapping table clearly and checking that each letter has a unique and consistent digit avoids such problems.

Final Answer:
Using the same letter to digit code as in TOAST and TRAIN, the word TORN is written as 5690.