# COMMENCE = 18251624, PRESERVE = 18323620, UNLAWFUL = what?

In a certain code language COMMENCE is coded as 18251624 and PRESERVE is coded as 18323620. How will UNLAWFUL be coded in that language?

This (https://brainly.in/question/57222899?cb=1718343468857) is a source of the question .

Attempt: The length of both the words and the encrypted number is 8 . Upon close inspection the positioning of letters do not seem to relate to the number in some fancy way.

• Is there enough information to be able to uniquely decrypt those numeric codes of 14 distinct letters? Commented Jun 13 at 21:19
• @WeatherVane I have just this information. BTW , how are you saying 14 distinct letters ? Aren't there 16 distinct letters ? Commented Jun 13 at 21:50
• What do you mean "do not seem to relate to the number in some fancy way"? Do they relate at all? Also, is this a one-to-one encryption? Meaning does COMMENCE correspond to 18251624 and no other numbers, and 18251624 can only be decrypted into COMMENCE and no other words? Commented Jun 13 at 22:35
• There are 14, but 16 would make it even worse. Commented Jun 13 at 22:44
• The only reference to this question I can find is this brain-teaser site. The question has two "answers". One is only a translation of the question and the other completely misses the point. Commented Jun 14 at 5:20

UNLAWFUL will be coded as:

24481236

Observations:

• All words have 8 letters and all codes have 8 digits, which might be coincidence.
• Only one of the letters in UNLAWFUL is in PRESERVE or COMMENCE.
• There is no direct correspondence of letters to digits.
• The digit 9 doesn't occur; 2 occurs four times; 1 occurs three times.

Some thoughts:

Splitting the numbers into prime factors does not yield any useful result. (The code might be the product of distinct primes, e.g. A = 2; B = 3; C = 5; ...; z = 101, but it isn't.)

The many 1's and 2's could mean that the code are just the alphabetical indices run together,so that CAT might be 3120. Of course, the code would usually be longer than the original word, but perhaps synonyms (start?, jelly?, illicit?) have been encoded. That's another dead end.

All words and codes have an even number of letters. Let's split them into pairs:

CO MM EN CE     PR ES ER VE
18 25 16 24     18 32 36 20

All numbers are composite. And code for the double letter MM is a square! (The codes for 16 and 36 are not double letters, but they could be 2×8 or 4×9. CO and PR share a code, but there are also several ways to get a product of 18.)

So, let's go with this for now: Each letter has a numerical value and the code for a pair of letters is the product of their values. This isn't hard to solve:

C = 6     E = 4     M = 5
N = 4     O = 3     P = 2
R = 9     S = 8     V = 5

Some letters get the same value, but that's probably okay. The code isn't unique anyway, since AB yields the same product as BA.

Unfortunately, that doesn't help with UNLAWFUL, because we don't have the numerical value of any of its letters except of N.

Wrapping it up:

Let's make a little table:

1 2 3 4 5 6 7 8 9
  P O E M C   S R
      N V       

Is there a password that we can use to find the numerical value of each letter? Or some other pattern? Let's tretch this out a bit:

1 2 3 4 5 6 7 8 9
      E   C     
  P O N M     S R
        V       

Now it's easy to see what's going on here. The compete table is:

1 2 3 4 5 6 7 8 9
H G F E D C B A .
Q P O N M L K J I
Z Y X W V U T S R

With this table and the rule to multiply the letter codes pairwise, we get:

UN LA WF UL
24 48 12 36

What happens when a word has an odd number of letters or when the product is smaller than 10? I don't know and I don't care – it's not part oft the assignment. :)