# Sum letters are not two different

The following letters all have something in common which may not be obvious at a first glance:

A B D H P


Hint

There are no misspellings or typos in the title of this question. Maybe a clue though.

Some great answers so far all of which I have upvoted but none of which are exactly what I am looking for.

Hint 2

The number 0 and the character ( also have the same property. I only said no other letters share it ;-)

Hint 3

As correctly identified by @RedBaron the ASCII table is key here. There is a good reason why "sum" is mentioned in the title and there are two reasons why "two" is mentioned.

• Are you sure B shouldn't be included too? – Deusovi Apr 18 '19 at 9:18
• @Deusovi You are indeed correct. I had missed that. I'll update the question. Thanks. – ElPedro Apr 18 '19 at 9:19
• Does a ! also share this property? – Eagle Apr 18 '19 at 12:04
• @Akari Yes it does. I have not listed them all. – ElPedro Apr 18 '19 at 12:06

The property seems to be related to:

Binary equivalents of the symbols/alphabets etc.

Explanation:

Binary equivalents for the following can be written as:
A -- 01000001
B -- 01000010
D -- 01000100
H -- 01001000
P -- 01010000
0 -- 00110000
( -- 00101000

So the property is,

The sum of digits in the binary equivalents is two

Or

The binary equivalents of all these have two 1s and six 0s.
Looking at the binary equivalents of the alphabets, one can see that no other alphabets share this property

The title (Thanks to @trolley813):

Two might refer to the sum of the digits, which is indeed two!
Title might mean that the sum [of digits in] letters is not different from two [but is equal to two]

The property is:

The index if each alphabet is equal to the sum of indices of the preceding alphabets in the sequence +1.

And,

There is no other alphabet with the index 1+2+4+8+16+1 = 32

• You've got it. Binary was what I was looking for but there are some other interesting patterns came out of this puzzle. I have added another hint in case anyone wants to have a go without looking at your answer. For the same reason, I'll wait a couple of hours before I accept it. well done! – ElPedro Apr 18 '19 at 12:26
• @Eagle Some refinement about the title, it probably should read "sum [of digits in] letters is not different from two [i.e. equals to 2]" – trolley813 Apr 19 '19 at 10:03
• Thanks a lot @trolley813 ! I've edited it – Eagle Apr 19 '19 at 11:15
• @trolley813 - Close but actually more of a play on words. Rot13(Fhz (Fbzr) yrggref ner abg gjb (gbb) qvssrerag) with Rot13(Fhz) and Rot13(gjb) giving clues to what I was looking for ;-) – ElPedro Apr 19 '19 at 14:51
• A bit contrived, I know, but left room for a couple of hints. – ElPedro Apr 19 '19 at 14:58

The property is that

each of their alphanumeric values (A=1, B=2, C=3...) is a power of 2.

• That wasn't what I was looking for but is indeed true and is possibly a side effect of the answer that I was looking for so +1 but I won't mark it as accepted yet. – ElPedro Apr 18 '19 at 9:23
• @ElPedro: It is a side effect, but it hinges on rot13(jurer gur nycunorg fgnegf ba gur NFPVV gnoyr. Vtaber gur svefg ovg bs gur NFPVV inyhr (orpnhfr vg vf nyjnlf 1 naq arire punatrf sebz N gb M), ohg QB erzrzore gung vg nyjnlf pbagevohgrf gb bar bs gur gjb 1-ovgf va lbhe vagraqrq nafjre. Vtabevat gur svefg ovg, N rssrpgviryl fgnegf ng ahzrevpny inyhr 1, naq rirel "cbjre bs gjb" yrggre nqqf rknpgyl 1 1-ovg gb gur pbhag, juvpu rkcynvaf jul obgu nafjref ner pbeerpg. Vs N unq fgnegrq ba n qvssrerag NFPVV inyhr, vg znl abg unir orra gur pnfr.) – Flater Apr 19 '19 at 8:21
• @Flater - Thanks for the explanation. It makes complete sense. As I said, some pretty interesting things have come out of what I at first though was a pretty simple puzzle :) – ElPedro Apr 19 '19 at 14:43

Is it

All the letters, symbols in this group have ASCII codes of form $$2^m + 2^n$$ where m and n are integers

Thus we have

From ascii code table,
$$A = 65 = 64 + 1 = 2^6 + 2^0$$
$$B = 66 = 64 + 2 = 2^6 + 2^1$$
$$D = 68 = 64 + 4 = 2^6 + 2^2$$
$$H = 72 = 64 + 8 = 2^6 + 2^3$$
$$P = 80 = 64 + 16 = 2^6 + 2^4$$

64 + 32 = 96 which does not correspond to any letter. The letter a begins at 97

$$0 = 48 = 32 + 16 = 2^5 + 2^4$$
$$( = 40 = 32 + 8 = 2^5 + 2^3$$

• Obviously moving in the right direction with the ASCII table. – ElPedro Apr 18 '19 at 12:20
• @ElPedro I guess Akari has formalized the informal property of my answer much better in his answer – RedBaron Apr 18 '19 at 12:22
• Still a good answer though :) – ElPedro Apr 18 '19 at 12:42
• I like the format of this answer more than the accepted one, simply because that's how I internally rephrased the accepted answer before even reading this one :) +1 – Flater Apr 19 '19 at 8:24

I think it's:

Each letter's alphanumeric value is double its predecessor, which also means, sum two times the alphanumeric value of the previous letter

This means that:

Starting from A=1 we get the sequence 1,2,4,8,16,... which corresponds to the sequence A,B,D,H,P

• Welcome! Again, a great answer but not exactly what I am looking for. +1 all the same. – ElPedro Apr 18 '19 at 12:14

Each time you add the position of the letter (A is 1 and B is 2), the next letter's position is the sum of the previous +1. Thus, 1+2 is 3, +4 is 7, +8 is 15, +16 is 31. You can't continue the problem because there are only 26 letters in the alphabet.