# My calculator seems to be broken

Damn... Here I am, in front of my examination paper, and my calculator is failing me! I can do some calculation, but for some additions, I don't get the good result! (I think my roommate purposefully changed something last night, as it was my turn to do the dishes and I, err, forgot to do it...)

Here are some calculations I just did :

18 + 34 + 28 + 6 = 33

27 + 15 + 15 + 68 = 29

22 + 7 = 50

Can you find what's going on with my calculator?

Edit/Hint : Wow, I just noticed something very strange :

28 + 34 + 6 + 18 = 86
15 + 27 + 15 + 68 = 125 and 68 + 27 + 15 + 15 = 125
7 + 22 = 29
All I did was the same calculation in another order, so I guess it might be important...

I also noticed that :

85 = 33 + 73 + 22 + 10

Hint 2: Just stumbled across other additions giving a wrong number :

47 = 14 + 116 + 68
6 = 20 + 37 + 8 + 7

Hey, listen, I have another one which is not making sense to me! But maybe it will help you...

54 = 54 + 7 + 8 + 7
54 = 54 + 102 + 7

Ok, time for the major hint before a bounty I guess :)...

My roommate just told me that he modified my calculator according to the subject of my examination! And it was :

chemistry.

Now, it might be easy. Chop-chop!

• is it settings change / change in hardware like LED screen ? – Amruth A Aug 3 '16 at 8:06
• "I think my roommate purposefully changed something" seems to suggest something like that – bg6471 Aug 3 '16 at 8:10
• More like something he could have changed programmatically. Obviously, some numbers are not representing their real values... – IAmInPLS Aug 3 '16 at 8:21
• All the digits are present so I guess it's not like missing segments, it's more like either some keyboard entries are swapped or some of the output numbers are swapped (or both). – rhsquared Aug 3 '16 at 8:31
• It might be significant that you get the right answer when the second number is greater than the first number and the fourth number is greater than the third. – Hugh Meyers Aug 3 '16 at 10:10

In your calculator, numbers are mapped to :

elements in periodic table and their abbreviations.

18 + 34 + 28 + 6 = 33

Ar + Se + Ni + C = Arsenic which is numbered 33 in the periodic table.

27 + 15 + 15 + 68 = 29

Co + P + P + Er = Copper = 29

22 + 7 = 50

Ti + N = Tin = 50

And of course, 7 + 22 = 29 because:

order is important!

85 = 33 + 73 + 22 + 10

Astatine = As + Ta + Ti + Ne

47 = 14 + 116 + 68

Silver = Si + Lv + Er

6 = 20 + 37 + 8 + 7

Carbon = Ca + Rb + O + N

Also, 54 = 54 + 7 + 8 + 7 and 54 = 54 + 102 + 7 because :

Xenon = Xe + N + O + N = Xe + No + N

• @IAmInPLS Oh, was trying to do same thing. Thanks. But couldn't figure out hint 1. 28 + 34 + 6 + 18 = 86. It doesn't fit. That's why I stopped a bit. – Lafexlos Aug 8 '16 at 13:24
• No problem, you got the answer anyway :). Hope it was entertaining enough for you! I think the last hint gave away much of the answer :) – IAmInPLS Aug 8 '16 at 13:28

Partial answer - much more like excluding some directions:

It cannot be

a simple (caesar cipher-like) digit replacement, because the right hand side of the first line could not start with a same digit as one of the terms on the left side.

I also think it has nothing to do with

binary, at least not something trivial. The binary representation of the three numbers in the last row are very different from each other.

Taking into consideration that the order of terms does matter, we can conclude that

the operation itself cannot be the usual addition. It is notes something what is not commutative.

• Yes. Watch out the tag lateral-thinking :) – IAmInPLS Aug 3 '16 at 8:39
• Ahh, so it looks up the numbers (discarding some to find a result if need be) in the OEIS, takes a random two digits from the listed sequence values and displays them - I see :) – Jonathan Allan Aug 3 '16 at 8:47
• Couldn't just the input be changed though and not the output? So the input values could follow digit replacement still. – slimeArmy Aug 4 '16 at 15:45
• @slimeArmy If $f(\text{"}22+7\text{"})=50$ and $f(\text{"}7+22\text{"})=29$ it can't be just digit to digit replacement, but still could be some kind of order induced digit to digit replacement, or replacement of the $+$ operator, or both with no output replacement as you suggest... – Jonathan Allan Aug 4 '16 at 15:53