In a certain code, ASSUMPTION is written as 1113472065. How is KNOWLEDGE…

Concept:

In many letter-to-number coding questions, each letter is replaced by a single digit derived from its position in the English alphabet (A = 1, B = 2, ... , Z = 26). The full position is reduced to one digit by adding its digits together, repeating the addition until a single digit remains — except that a position which is an exact multiple of 9 is written as 0, not 9 (equivalently, the position taken modulo 9).

Application:

1. Confirm the rule using the clue: ASSUMPTION is coded as 1113472065.

   Letter	Alphabet position	Reduced digit
   A	1	1
   S	19	1
   S	19	1
   U	21	3
   M	13	4
   P	16	7
   T	20	2
   I	9	0
   O	15	6
   N	14	5

   Reading the reduced digits in order gives 1 1 1 3 4 7 2 0 6 5, i.e. 1113472065 — exactly the code given for ASSUMPTION, so the rule is confirmed.

2. Apply the same rule to every letter of KNOWLEDGE.

   Letter	Alphabet position	Reduced digit
   K	11	2
   N	14	5
   O	15	6
   W	23	5
   L	12	3
   E	5	5
   D	4	4
   G	7	7
   E	5	5

   Reading these reduced digits in order gives 2 5 6 5 3 5 4 7 5, i.e. 256535475.

3. Cross-check 256535475 against the four values on offer: it matches the value 256535475 digit-for-digit, while every other value on offer differs from it in at least one digit.

So KNOWLEDGE is coded as 256535475.