Almost half a million, yet smaller than a hundred

Question

Consider, for example, the number 420109. It's quite big, isn't it? Not so far from half a million. Yet it can be interpreted to be smaller than a hundred with a very simple trick, without putting any mathematical operators between the digits, without using any mathematical function on it, and without erasing or hiding parts of it.

How?

Hint 1

There are a few other 6-digit numbers this could work with, but not many.

Hint 2

Not only can it "be made smaller", 420109 actually is smaller than 100 from a certain viewpoint. There are very few 6-digit numbers where this can be applied.

Sorry for the ambiguous formulation. I meant 100 as a number. The "a" in "a hundred" was superfluous. I corrected it now. — vsz, Jan 14 '20 at 09:00
rot13(Vf vg eryngrq gb n qngr, r.t. ner gur 4 zvqqyr qvtvgf "2010")? — Earlien, Jan 14 '20 at 11:33
In my opinion hint 1 shouldn't be a hint, it restricts the possible solutions (see @CG. answer; it works but not with the hints) so it should be part of the main riddle — Gilsido, Jan 14 '20 at 16:41
@Gilsido isn't the whole point of a hint to restrict the possible solutions? — JakeRobb, Jan 14 '20 at 22:12
@JakeRobb I'm sure that the point of a hint is not restricting the possible solutions, but to restrict our focus to get the solution. A puzzle with many possible solutions are highly discouraged (and may be closed as "too broad".) A puzzle should have a single correct solution, and hints are given to make us easier getting that correct solution. — athin, Jan 15 '20 at 05:31
Based on the title, I wanted the answer to be "milli-" as a prefix meaning 1/1000, but also about half of the word "million" :( — maxathousand, Jan 15 '20 at 15:13
Edit: Changed the wording to be less ambiguous, as that word seemed to be the most likely cause why people voted to close. — vsz, Dec 22 '22 at 08:20
I like the edit, it makes the puzzle way more approachable. Voting to reopen, again. — Bass, Dec 22 '22 at 19:50

Bass · Accepted Answer · 2020-01-14T15:02:52.643

100

Pardon my French, but no whole number smaller than 100 can be larger than 99, so this puzzle must be completely and utterly

brilliant, because 99 is "quatre-vingt-dix-neuf" or "four-twenty-ten-nine" in French.

edited Jan 14 '20 at 15:02

answered Jan 14 '20 at 14:37

Bass

77,343
8
173
360

5

This one has to be right! Great thinking – gabbo1092 Jan 14 '20 at 14:41
44

A puzzle, created only for those who speak French. Sadly, I'm not among them. – rhsquared Jan 14 '20 at 16:51
6

Rot13(Ba orunys bs gur Serapu crbcyr, V jbhyq yvxr gb ncbybtvfr gb nyy gubfr jub unq gb yrnea gb pbhag gb n uhaqerq va bhe ynathntr...) – Jan 14 '20 at 19:48
4

I still don't get it. – Aleksandr Hovhannisyan Jan 15 '20 at 16:24
@AleksandrH - Rot13(Ybbx hc gur Serapu ahzorevat ehyrf. Hayvxr va Ratyvfu, jurer lbh fnl "avargl" gura "avar" sbe avargl-avar, va Serapu gurl fnl "sbhe gjraglf, n gra, naq n avar" gb trg avargl-avar. ...urapr eru-cs' pbzzrag.) – BruceWayne Jan 15 '20 at 17:40
1

The only reason why I get this one is because of Diebuster and its Buster Machine nomenclature. – Eriol Jan 15 '20 at 17:48
@eru-cs, Vg'f abg ernyyl gung onq. Hc gb 69, vg'f gur fnzr va Serapu va Ratyvfu. Gur bayl jrveqarff vf gung 70-79 vf 6-10..6..19 vafgrnq bs 7,7-1..7-9. Fnzr sbe gur 90'f. Bar fvzcyr yvggyr qvssrerapr sebz Ratyvfu. – ikegami Jan 15 '20 at 21:00

score 35 · Answer 2 · answered Jan 14 '20 at 11:03

35

Lateral thinking here:

The 010 part of the number looks like a % symbol, so the number could be viewed as 42 % 9 which is less than 100.

answered Jan 14 '20 at 11:03

JS1

17,874
3
52
103

1

Wow! Just wow! I never thought of that. It violates some of the hints (it would be a mathematical operator), but still, you get the +1 for the idea. – vsz Jan 14 '20 at 13:52
5

JS1 isn't "putting" operators anywhere; JS1 is misinterpreting something already there as an operator. – ralphmerridew Jan 14 '20 at 15:23
That operation will only be recognized to programmers who work in a C-based language. To most other people (including mathematicians), it'll be gibberish. – BlueRaja - Danny Pflughoeft Jan 14 '20 at 15:30
2

% is used in a lot of other programming languages as well, but your point remains valid. – Skylar Jan 14 '20 at 16:56
13

As someone that knows C but not French, I'm upvoting this one. – Cristobol Polychronopolis Jan 14 '20 at 17:44
6

@BlueRaja-Danny: I think most others would interpret it as 42% of 9, which still works. – Nick Matteo Jan 14 '20 at 20:04

score 34 · Answer 3 · answered Jan 14 '20 at 08:08

34

Well, seeing that this is lateral thinking:

You wrote 420109 using 6 digits, and a hundred using 7 letters. So, it's smaller.

answered Jan 14 '20 at 08:08

CG.

2,590
12
25

nice thinking, but I didn't say shorter, but smaller. – vsz Jan 14 '20 at 09:01
30

I would claim smaller = shorter for a word, but ok. :-) – CG. Jan 14 '20 at 09:46

SMR · Answer 4 · 2020-01-14T14:54:07.483

26

Following up on @Earlien answer I think the trick is to

decompose 420109 as 4 20 10 9 and read it in French

This gives

99 = 4*20 + 10 + 9 which is one unit less than 100

Similarly

420108 would read as 98

edited Jan 14 '20 at 14:54

answered Jan 14 '20 at 14:40

SMR

935
5
7

This is definitely the right answer. – Ian MacDonald Jan 14 '20 at 15:25
Yes indeed, that's definitely how they read it, no trick involved :) – vsz Jan 14 '20 at 18:43
7

Oh, I sniped you by just over 2 minutes? Good thing I didn't notice the question was 7 hours old when I hurried to answer, then. :-) As per tradition, +1 to you too. – Bass Jan 14 '20 at 18:53

score 15 · Answer 5 · answered Jan 14 '20 at 13:24

15

Is it the way it’s read?

Four “20’s” and 1 “09” = 89

answered Jan 14 '20 at 13:24

Earlien

1,878
4
33

This has to be it. – F1Krazy Jan 14 '20 at 13:28
If it is, Hint 1 seems misleading. – Earlien Jan 14 '20 at 13:30
I wouldn't say that. There are 900,000 6-digit numbers, and this will work for maybe 0.1% of them. – F1Krazy Jan 14 '20 at 13:32
4

At least it's closer than all the other answers. The real answer is much more self-evident, however, it might require some knowledge not all of us have. – vsz Jan 14 '20 at 13:54
2

@vsz In that case, does the question perhaps require the [tag:knowledge] tag? – F1Krazy Jan 14 '20 at 14:14
Whoever likes this answer will probably also enjoy my mathematical posts on "self-describing" numbers, which use a very similar principle: https://projectatmos.space/profile/1p8WCZnqqG6N3ZOsJxBgUTo/p1cNCw1OTsioTQBRk – Fabian Röling Jan 16 '20 at 17:35

score 10 · Answer 6 · answered Jan 14 '20 at 11:21

10

This is a really silly idea, but:

Put a minus sign before it to make it -420109. It's smaller than 100, and technically speaking, I haven't put a mathematical operator between the digits.

It obviously doesn't fit the first hint, but it adheres to the wording of the actual puzzle.

answered Jan 14 '20 at 11:21

F1Krazy

8,048
1
33
62

Nice idea but by that logic all of the positive numbers (six digit or otherwise) could be made smaller than 100. – Abbas Jan 14 '20 at 14:12

score 9 · Answer 7 · answered Jan 14 '20 at 14:27

9

Well... there's always...

100
_{^{_{⁴²⁰¹⁰⁹}}}

Doesn't seem to mesh with the idea that there are very few of these 6-digit numbers that work, though.

answered Jan 14 '20 at 14:27

Ian MacDonald

12,806
1
33
63

score 8 · Answer 8 · edited Jan 14 '20 at 16:35

8

Although I really like Bass' idea, I want to offer another, rule-bending, idea:

Put in a decimal point (or a comma, depending where you live) and make it 4.20109

Now the number is definitely below 100 without breaking the rules:

- Putting in a single pixel is as easy as it gets (and we don't need to learn another language!)
- Not a mathematical function
- No hiding or erasing of numbers
- Not a mathematical operator (although a mathematical symbol)

edited Jan 14 '20 at 16:35

F1Krazy

8,048
1
33
62

answered Jan 14 '20 at 15:58

Jan T.

81
1

1

Nice thinking, but it wouldn't satisfy Hint 1. – Earlien Jan 15 '20 at 00:49
1

True, I did not take the hints into account. – Jan T. Jan 15 '20 at 08:33

score 7 · Answer 9 · answered Jan 14 '20 at 08:21

7

Two possible solutions:

- It is smaller than a hundred, if you write "a hundred" very large.
- It is smaller than a hundred of itself (or of some other unspecified quantity).

answered Jan 14 '20 at 08:21

Deusovi

146,248
16
519
609

score 6 · Answer 10 · answered Jan 14 '20 at 14:37

I think the answer is

49

Because

The first thing I saw was how the shapes of the letters match up. By transposing the 2 on the top of the 4, it becomes a funky looking 4, but still a 4. Then place the 1 on it as well. Still a 4. Then the 0's can be slightly shrunk and placed on top part of the nine.

I hope I'm at least on the right track. Otherwise, I'm crazier than I thought.

Sorry, in a rush. I was the best picture I could do:)

score 6 · Answer 11 · answered Jan 15 '20 at 18:57

6

₄₂₀₁₀₉

 1       00      00
 1      0  0    0  0
 1      0  0    0  0
 1       00      00

answered Jan 15 '20 at 18:57

Acccumulation

1,018
5
12

3

This has ended up in the "low quality" queue, but it seems like an okay answer to me as it's using a literal definition of "smaller". – F1Krazy Jan 15 '20 at 19:45

score 5 · Answer 12 · edited Jan 14 '20 at 21:08

5

No trick involved, because

it is almost half a million but certainly a lot smaller than hundred (millions).

edited Jan 14 '20 at 21:08

F1Krazy

8,048
1
33
62

answered Jan 14 '20 at 18:23

QBrute

1,178
9
13

score 4 · Answer 13 · answered Jan 14 '20 at 19:46

4

420109 is 19

in base 420100

or

in the list of multiples of 22111... I was hoping this was a Prime thing....

answered Jan 14 '20 at 19:46

Tezra

181
4

score 3 · Answer 14 · answered Jan 14 '20 at 12:57

This is the stupidest solution I've ever cooked up, but here it is anyway.

Turn the 1 sideways to make it a divisor for a fraction. Now you get 420/09, which comes out to be way less than 100. This is, of course, monumentally stupid and I hate it. If it's the right answer, I will be sad.

Almost half a million, yet smaller than a hundred

14 Answers14