My friend Beto and I constantly buy things for one another. One day, he gave me a strange-looking phone and said it was my birthday gift (My birthday wouldn't be until 3 more months). He said he bought it from some weird store and it was made from some company called Jasoom; I, of course, never believed him, but I kept the gift anyways as a token of his appreciation.

Years later, while rummaging through some of my old things, I happened to find this phone again! Reluctantly, I turned it on, finding out that I had received a single text message. It read:


I stood and stared for a moment until I discovered what the other person was asking, only to realise that the phone I had was using a different set of keys --- apparently whoever manufactured my phone installed the keypad backwards! I fumbled with the controls until I produced a half-hearted response, which said:


I was a bit worried at first if I mistranslated their message (or if they would even bother with a response well after they sent their original message), but much to my chagrin the person on the other end responded in less than 10 seconds flat! I knew for sure they understood me, because this was their response:


Months went by until they texted me again, although this time with a far-more alarming question, which read:


I was completely flabbergasted, so I offered the only response that made the most sense:


Quite the "close encounter", wouldn't you say? Anyways, while texting my compatriot, I realised something I never noticed before:

One of the labels on the keypad was scratched off (didn't I say this phone was poorly made?), so I could not read what it originally said. Fortunately, I never used the key during my friendly discussion, but I would still like to know what was that missing label... perhaps you could help?

You only need to give me the sequence that was used for the label, not the corresponding letters; however, I'll show preference to any answer that explains which characters were used as well.

Edit: Turns out I made a mistake in my original, hand-written notes and accidentally mixed up one of the key sequences when encrypting; it's fixed now, but I wanted to inform all of you who may still be working on the problem before you get led too far astray.

I apologize for any confusion.


While it may not be immediately obvious, when I wrote 6274852852 and my compatriot wrote 6947369369, we were saying the same thing; however, when they wrote 6947472725, nothing matched what I wrote.

Just to be clear, we were both talking about me... and I kinda lied (something matches, but not the whole).

Funny thing I realized, though, following my conversation: if, perhaps, this phone was manufactured by a different company named Barsoom, my last response should probably have been 59697338523852... and – even more surprising – I still would not have used the unlabeled key!

I think it's necessary to remind you that this is a phone; as such, keypads should have labels of only one of two different lengths (or three, if you're being a smart-alec about characters). Of course, I'm not telling you how long the missing sequence is, but perhaps that narrows down the field considerably.

Still not convinced? Fine, think about how a normal phone-pad is arranged, then think about how it's labeled; you should be able to find the numbers that are missing this way, but this may not be enough to tell you how they are ordered or which key indicates which sequence.


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