In a certain code language, 'DEMAND' is written as ‘410132144' and 'SUPPLY' is written as '194216161225'. How will 'PRODUCT' be written in that language?

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Accepted Answer

Step 1: Analyze the given codes.
- DEMAND -> 410132144
- SUPPLY -> 194216161225

Step 2: Assign numerical values to letters (A=1, B=2, ..., Z=26).
DEMAND: D(4), E(5), M(13), A(1), N(14), D(4)
SUPPLY: S(19), U(21), P(16), P(16), L(12), Y(25)

Step 3: Observe the code for DEMAND: 410132144
Split into pairs or single digits:
4 10 13 21 4 4
Check if these correspond to letters:
4 -> D
10 -> J (not E)
13 -> M
21 -> U (not A or N)
4 -> D
4 -> D
This suggests the code is not direct letter to number mapping.

Step 4: Check if each letter is coded as the product of its position and its alphabetical value.
For DEMAND:
Positions: 1 2 3 4 5 6
Letters: D(4), E(5), M(13), A(1), N(14), D(4)
Multiply position * letter value:
1*4=4
2*5=10
3*13=39
4*1=4
5*14=70
6*4=24
Now check the code: 410132144
Split as: 4 10 13 21 44
But 13 and 21 do not match 39 and 70.

Step 5: Check if the code is concatenation of position * letter value:
DEMAND: 4 10 39 4 70 24
Concatenate: 4103947024 (not matching 410132144)

Step 6: Check if the code is position + letter value:
1+4=5
2+5=7
3+13=16
4+1=5
5+14=19
6+4=10
Concatenate: 571651910 (not matching)

Step 7: Check if the code is letter value followed by position:
D(4)1, E(5)2, M(13)3, A(1)4, N(14)5, D(4)6
Concatenate: 41513211456 (not matching)

Step 8: Check the code for SUPPLY:
S(19), U(21), P(16), P(16), L(12), Y(25)
Code: 194216161225
Split as: 19 42 16 16 12 25
Notice 42 is not a letter value.

Step 9: Hypothesis: The code is letter value followed by letter value + position.
For DEMAND:
D(4), E(5), M(13), A(1), N(14), D(4)
Positions: 1 2 3 4 5 6
Try: letter value + (letter value + position)
D: 4 and 4+1=5 -> 45 (not matching 4 or 10)

Step 10: Another approach: The code is letter value followed by position squared.
DEMAND positions squared: 1,4,9,16,25,36
Check code: 4 10 13 21 44
No match.

Step 11: Check code for SUPPLY:
19 42 16 16 12 25
Note 42 is 21*2, 19 is S, 42 is double of U(21)
So maybe code is letter value and double letter value for vowels?
U is vowel, 21 and 42
Check DEMAND vowels: E(5), A(1)
Code: 4 10 13 21 44
10 and 21 could be double of 5 and 10.5 (no 10.5)

Step 12: Try splitting DEMAND code differently:
4 10 13 21 44
4 (D), 10 (J), 13 (M), 21 (U), 44 (not letter)
No match.

Step 13: Check if code is letter value followed by letter value + previous letter value.
DEMAND:
D(4)
E(5) + D(4) = 9
M(13) + E(5) = 18
A(1) + M(13) = 14
N(14) + A(1) = 15
D(4) + N(14) = 18
Code: 4 10 13 21 44
No match.

Step 14: Since the code for DEMAND is 410132144, split as 4 10 13 21 44
Check if 21 is N(14) + 7
44 is 4*11
No clear pattern.

Step 15: Check if code is letter value concatenated with position*letter value:
D(4), 1*4=4 -> 44
E(5), 2*5=10 -> 510
M(13), 3*13=39 -> 1339
No match.

Step 16: Check if code is letter value followed by letter value + position:
D(4), 4+1=5 -> 45
E(5), 5+2=7 -> 57
No match.

Step 17: Check if code is letter value followed by letter value - position:
D(4), 4-1=3 -> 43
No match.

Step 18: Since the code for SUPPLY is 194216161225, split as 19 42 16 16 12 25
19 = S
42 = 2*21 (U)
16 = P
16 = P
12 = L
25 = Y
So for vowels, code is letter value and double letter value.

Step 19: For DEMAND vowels E(5) and A(1), check if code has 10 and 2 (double values)
Code: 4 10 13 21 44
10 could be double of 5 (E)
21 could be double of 10.5 (no)

Step 20: Since the code for DEMAND is 410132144, and SUPPLY is 194216161225, the pattern seems to be:
For each letter, write its alphabetical position, then if vowel, write double of its position.

Step 21: DEMAND letters and code parts:
D(4) - 4
E(5) - 10 (double 5)
M(13) - 13
A(1) - 2 (double 1)
N(14) - 14
D(4) - 4
Concatenate: 4 10 13 2 14 4 = 410132144 (matches)

Step 22: SUPPLY letters and code parts:
S(19) - 19
U(21) - 42 (double 21)
P(16) - 16
P(16) - 16
L(12) - 12
Y(25) - 25
Concatenate: 19 42 16 16 12 25 = 194216161225 (matches)

Step 23: Now encode PRODUCT:
P(16) - consonant -> 16
R(18) - consonant -> 18
O(15) - vowel -> double 15 = 30
D(4) - consonant -> 4
U(21) - vowel -> double 21 = 42
C(3) - consonant -> 3
T(20) - consonant -> 20
Concatenate: 16 18 30 4 42 3 20 = 161830442320

Step 24: Check options:
Option 1: 161830442320 (matches)
Option 2: 323615821640
Option 3: 161542320
Option 4: 161815421320

Answer is option 1.

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