# Almost half a million, yet smaller than a hundred [closed]

Consider, for example, the number 420109. It's quite big, isn't it? Not so far from half a million. Yet it can be made 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 at 9:00
• So it can be made smaller than 100? – CG. Jan 14 at 9:48
• 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 at 16:41
• @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 at 5:31
• 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 at 15:13

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.

• This one has to be right! Great thinking – gabbo1092 Jan 14 at 14:41
• A puzzle, created only for those who speak French. Sadly, I'm not among them. – rhsquared Jan 14 at 16:51
• 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...) – eru-cs Jan 14 at 19:48
• I still don't get it. – AleksandrH Jan 15 at 16:24
• The only reason why I get this one is because of Diebuster and its Buster Machine nomenclature. – Eriol Jan 15 at 17:48

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.

• 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 at 13:52
• JS1 isn't "putting" operators anywhere; JS1 is misinterpreting something already there as an operator. – ralphmerridew Jan 14 at 15:23
• % is used in a lot of other programming languages as well, but your point remains valid. – Skylar Jan 14 at 16:56
• As someone that knows C but not French, I'm upvoting this one. – Cristobol Polychronopolis Jan 14 at 17:44
• @BlueRaja-Danny: I think most others would interpret it as 42% of 9, which still works. – Nick Matteo Jan 14 at 20:04

Well, seeing that this is lateral thinking:

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

• nice thinking, but I didn't say shorter, but smaller. – vsz Jan 14 at 9:01
• I would claim smaller = shorter for a word, but ok. :-) – CG. Jan 14 at 9:46

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

• This is definitely the right answer. – Ian MacDonald Jan 14 at 15:25
• Yes indeed, that's definitely how they read it, no trick involved :) – vsz Jan 14 at 18:43
• 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 at 18:53

Is it the way it’s read?

Four “20’s” and 1 “09” = 89

• This has to be it. – F1Krazy Jan 14 at 13:28
• If it is, Hint 1 seems misleading. – Earlien Jan 14 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 at 13:32
• 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 at 13:54
• @vsz In that case, does the question perhaps require the knowledge tag? – F1Krazy Jan 14 at 14:14

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.

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

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).

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.

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)

• Nice thinking, but it wouldn't satisfy Hint 1. – Earlien Jan 15 at 0:49
• True, I did not take the hints into account. – Jan T. Jan 15 at 8:33

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:)

420109

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

• 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 at 19:45

420109 is 19

in base 420100

or

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

No trick involved, because

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

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.