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This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and their spin-off What is a Number™ series.

An entry into the 20th fortnightly topic challenge.

Main puzzle:

If a number conforms to a certain rule, I call it a Frightful Number™. Use the following examples to find the rule:

Frightful Numbers™ Non-Frightful Numbers™
15 23
427 487
729 512
2016 6210
13579 24680
492717 638424
1837591 4295354
43728161 15594260
1010101010 1001001001
1738629405 7293548016
46819275183 62571139572
92729092729 72627472627
7070707070707 4141414141414

Here is a CSV:

Frightful Numbers™,Non-Frightful Numbers™
15,23
427,487
729,512
2016,6210
13579,24680
492717,638424
1837591,4295354
43728161,15594260
1010101010,1001001001
1738629405,7293548016
46819275183,62571139572
92729092729,72627472627
7070707070707,4141414141414

The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is a Frightful Number™ on its own. In particular, a number's relationship to other numbers in the sequence is irrelevant.

These are not the only examples of Frightful Numbers™ (or non-Frightful Numbers™), more can be found.

Hints:

  1. The title of the puzzle is a synonym for the required property - this is to ensure that it isn't too easy (it would be if I gave you the word)

  2. The whole number being Frightful™ is a property of its parts

Bonus Puzzle!

(For those like Deusovi who don't find normal What is a Number™ puzzles interesting enough)

Frightful Numbers™ and Not Frightful Numbers™ have a real-world application.

Your challenge is (assuming you have found an answer to the main puzzle) to find what this could be ... It's not too hard to think of if you have the correct answer.

I think I might have missed the Halloween boat on this one... Oh well...

Here's hoping I don't make another silly mistake like last time!

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  • $\begingroup$ What's wrong with the question, @downvoter? $\endgroup$
    – boboquack
    Nov 23, 2016 at 7:17
  • $\begingroup$ Wasn't me who downvoted - I don't particularly like "What is a _____ Number™" clues since there aren't as many interesting non-obscure properties to exploit with numbers instead of words. I suspect the downvoter felt the same way. $\endgroup$
    – Deusovi ♦
    Nov 23, 2016 at 7:31
  • $\begingroup$ @Deusovi Well then here's hoping that it is interesting enough for you. It's definitely not very obscure, but does require lateral thinking (not enough though to warrant that tag). $\endgroup$
    – boboquack
    Nov 23, 2016 at 7:34
  • $\begingroup$ Are all numbers either Frightful (tm) or Not Frightful (tm), or are some numbers neither? (The names suggest that Not Frightful = not Frightful, but the comment about real-world applications suggests maybe both are names of special categories of number.) $\endgroup$
    – Gareth McCaughan ♦
    Nov 23, 2016 at 17:33
  • 6
    $\begingroup$ oh i know this one! ... because 7 8 9! $\endgroup$
    – monoRed
    Nov 24, 2016 at 21:10

2 Answers 2

Reset to default
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My answer:

Frightful Numbers™ are numbers that don't contain consecutive digits that are either the same or directly adjacent on a telephone keypad:
123
456
789
--0 (0 should be aligned directly below the 8)
They are called Frightful Numbers™ because they are afraid of their neighbors/constantly on the run?? (not sure about this yet)

Examples:

One example to show the non-connectedness of the frightful numbers I've tried to draw here: (this is for the number 1738629405, consecutive lines have been giving alternating colors, red-blue-red-...)
Telephone number pad
The counterexamples are a lot easier to "show", as I've tried to do here below: (left is the not-frightful number itself, right is where it "connects"):
23 (2-3)
487 (8-7)
512 (1-2)
6210 (2-1)
24680 (8-0)
638424 (6-3)
4295354 (5-4)
15594260 (5-5)
1001001001 (0-0)
7293548016 (5-4 and 8-0)
62571139572 (1-1 and 2-5)
72627472627 (7-4 and 4-7)
4141414141414 (4-1 and 1-4)

About the real world application:

I don't know about this yet, or maybe the usage on phone number pads is already what is meant by the application, although this is more of an occurrence than it is an application.

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  • $\begingroup$ That's smart! +1 :) Should be the accepted one! $\endgroup$
    – Techidiot
    Dec 1, 2016 at 16:33
  • $\begingroup$ I'll give you the tick, but do try the bonus. Think of other places the number pad is used and the effect of having a frightful number in that application. $\endgroup$
    – boboquack
    Dec 1, 2016 at 18:50
  • $\begingroup$ It seems that frightful numbers would make for worse PIN codes, because if someone were spying on you while you enter your code, non-frightful numbers allow you to easily hit 2 buttons without it being noticeable that you hit them both or which order you did. $\endgroup$
    – GendoIkari
    Feb 12, 2018 at 22:30
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For the bonus question:

Frightful Numbers™ are used to store or write (or otherwise communicate) the phone unlock patterns -- consider the one shown in this image: pad
A: quick, I need to use your phone, how do I unlock it?
B: well, you need to enter a pattern, that's ugh... a sort of L starting from ugh... it's difficult to explain... if it was a PIN I would just tell you the numbers, I wish we had something similar for the patterns!
A: actually we have! Quick, tell me the sequence encoded using Frightful Numbers™!
B: that would be 1478
A: it worked! Thank God we have Frightful Numbers™!

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  • $\begingroup$ If anything, this would be the antithesis of Frightful Numbers™, as Frigthful Numbers™ specifically do not have adjacent digits. Also, unlocks like these can go diagonally as well, I think. (Correct me if I'm wrong!) Frightful Numbers™ do not account for diagonals in their rule. $\endgroup$
    – Someone
    Jun 17 at 22:42

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