Wikipedia:Reference desk/Archives/Mathematics/2006 August 16

The Mint puzzle
I'm reluctant to place this in 'mathematics', but it vaguely qualifies. A British television quiz show has been running this competition for weeks now:

Add the numbers:

NINETEEN MINUS FIVE =

4 + 3 x 2 =

6 - 5 =

Answer is 2106. The caller won £36000 on 3/10/06 show. Possible money to be won has been higher than £100,000.

Hundreds of incorrect guesses have been registered. Read them here.

[04/10/06] 2:20AM - This puzzle has been solved at last! A caller correctly guessed the number '2106' and won £36,000 for her trouble. No information was given as to how the answer was reached; only it was mentioned that other callers had been close to this caller's number on a couple of occassions, and that this caller had watched "for weeks", attempting to find the answer.

My next guess will be 1071, adding all the numbers, plus the addition nine in nineteen, plus all the roman numerals (inc. X) contained therein. Can anyone think of another 'logical' answer, not already guessed? Dmn € &#1332;&#1396;&#1398; 00:42, 16 August 2006 (UTC)


 * I'm afraid I don't quite follow. Which numbers are supposed to be added? Black Carrot 05:48, 16 August 2006 (UTC)
 * It's part of the puzzle that you have to figure that out. Most likely it's something really stupid, having nothing to do with maths. --Lambiam Talk 07:10, 16 August 2006 (UTC)
 * Shouldn't that be "nineteen"? --Lambiam Talk 07:03, 16 August 2006 (UTC)


 * Maybe that's also a part of the puzzle :-) As Lambiam suggested, there is of course only one correct answer, 25, and anyone can create as many crazy interpretations as he desires. However, here's a few more to think of: Adding the Ascii codes of the characters (this has several variations based on how you treat spaces and newlines), and adding the numerals and gematrical values of the letters. -- Meni Rosenfeld (talk) 07:37, 16 August 2006 (UTC)


 * I would agree with 25, but strangely it is listed on the page as a wrong answer? - Rainwarrior 18:16, 16 August 2006 (UTC)


 * Suppose I find the right answer, say 33. Is there any way of then obtaining conformation that this is the right answer? Or if it is wrong, any way of finding that out? --Lambiam Talk 08:45, 16 August 2006 (UTC)


 * Well the obvious answer would be 25, but as it seems to be some sort of silly puzzle it could be the sum of all the numbers mentioned without reference to the operators (giving 44), or it could be a mixture of both (giving 69).


 * Or it could be that everything is in base 36, so NINTEEN = 31043602706, etc. Or maybe everything is encoded with ROT13. Or maybe the quizzer doesn't have a particular solution in mind, but only wants to see how far people will go in their search for an answer. -- Meni Rosenfeld (talk) 11:23, 16 August 2006 (UTC)


 * Sorry, it should read NINETEEN. Dmn € &#1332;&#1396;&#1398; 17:48, 16 August 2006 (UTC)


 * Rainwarrior: If 25 wasn't listed as a wrong answer, we wouldn't be having this discussion, would we? -- Meni Rosenfeld (talk) 19:14, 16 August 2006 (UTC)


 * "Name a Bone?" "Err.. tibia!" "Wrong the right answer was femur."   The question doesn't give enoth infomation to reach the right answer without some form of guessing.Seo42 23:32, 16 August 2006 (UTC)


 * It sounds a bit like Marvin's question in one of the Hitchhiker books:
 * "...I am at a rough estimate, thirty billion times more intelligent than you. Let me give you an example. Think of a number, any number." [said Marvin]
 * "Er, five" said the mattress.
 * "Wrong," said Marvin. "You see?"Black Carrot 05:40, 17 August 2006 (UTC)


 * Although, to be fair, questions like this usually have a clever enough "right" answer, that seems inherent enough when it's pointed out, to not be too irritating in the long run. Black Carrot 05:41, 17 August 2006 (UTC)


 * Could it be something like :

NINETEEN + MINUS +  FIVE

....... -- DLL .. T 18:26, 19 August 2006 (UTC)


 * It certainly could. Or it could be a subliminal numerological message planted by the Illuminati to control the world. Is that a risk we want to take? I think not. Black Carrot 03:27, 21 August 2006 (UTC)

I think the real answer is coupled to the quiz being a total ripoff designed to separate idiots credulous folk from their money. I assume that possible answers have to be phoned at premium rates - no right answer will have been decided on until enough money has come in, then a really obscure one will be selected. 81.153.219.1 15:42, 22 August 2006 (UTC)

TRUE TRUE the show is a rip off but very addictive as i want to know what number they will choose and how they will justify it !!

I reckon its:

1943265. FIVE is purposely omitted. nc.wd.irl.dec.5.1983

The "beauty" of this puzzle is that there are so many possible answers, all of which could be deemed correct. Indeed I believe that ITV simply think of lots of different answers and cross them off when people guess them on-air such that they wait until one remains. I dont know if anyone has considered adding the = signs as 11 on their sides. Or adding the - sign as a 1 on its side. Matt Cargill ---

The presenters do have a Golden Envelope with the answer in, so they can't be letting it just carry on until they get bored. (Or filthy rich.) For all we know, they could want us to add all the numbers on the screen, which would include the telephone number! This question is going to last ages, and is really bloody annoying. The most annoying thing is watching the presenters looking uncomfortable like there's no one phoning in, no doubt luring people in who assume they'll get straight on air, when of course they have tons of people on the line. Tom - My solution as follows includes roman numerals

from the question line m in numbers gives 1000

from the nineteen minusfive line nineteen            19 five                 5 I                    1 I                    1 I                    1 M                 1000 IV                   4 V                    5 nineteenminusfive   14 gives 1050

from the next line 4                    4 3                     3 2                     2 (4+3)x2              14 4+(3x2)             10 gives  33

from the last line 6 (in isolation)     6 5 (in isolation)     5 6-5                  1 6+5 (adding numbers) 11 gives  23 all lines Totals                  2106 ==== Sneaky 1000 in question and counting 6&5 twice but not 4&3&2. There may be another way of doing it but I have not discovered it! Garth - I think Garth was close -- but got a bit lost near the end. (Edit this item (link on top right corner of section) to see text lined up!) Don't count anything from "add these numbers" question line! Answer the questions first and use letters or numbers to match. The first line gives :- "nineteen minus five = fourteen" nineteen            19 five                 5 fourteen            14 nine                 9 four                 4 I                    1 I                    1 I                    1 M                 1000 IV                   4 V                    5 MI                1001 Total from first line is 2064

The second line gives :- "4 + 3X2 = 10" 4                    4 3                     3 X                    10 2                    2 10                   10 1                     1 0                     0 Total from second line is 30

The third line gives :- "6-5=1" 6                    6 5                     5 1                     1 Total from third line is 12

Overall total is 2064 + 30 + 12 = 2106 --- Voila! Simple eh! William Donaghy

I remain unconvinced there's a sensible solution
I created a spreadsheet for the possible inputs, and although a no. of them make 2106, none of them are really consistent, and I don't currently believe that that can ever be the case.

Here's my `best' effort:

(use)              1     1    1       0    1    1    1     1    1    1     1 NINETEEN MINUS FIVE    19    5    14      9    1    1000 1001  1    1    4     5      2051 (why)             “19”  “5”  “19-5”  “9”  “I”  “M”  “MI”  “I”  “I”  “IV”  “V” (use)              1    1    1    0      0      1          1          1 4 + 3 X 2              4    3    2    7      6      14         10         10          43 (why)             “4”  “3”  “2”  “4+3”  “3x2”  “(4+3)x2”  “4+(3x2)”  “X” (use)              1       1    1 6 – 5                  6       5    1                                                 12     (why)              “6”     “5”  “6-5” 2106

But this excludes the "NINE" (9) input, for no real reason. --Neil 11:07, 5 October 2006 (UTC)

Ordering of the natural numbers order-isomorphic to ε0
I've been trying to get a grip on the countable ordinal numbers by constructing orderings of the natural numbers order-isomorphic to them, for example 2,3,4... 1 for ω + 1, and 1,3,5... 2,4,6... for 2ω. So far I've managed to get up to any ordinal of the form $$\omega^{\omega^{\omega^{...}}}$$ by using the fundamental theorem of arithmetic, but I can't think of any ordering isomorphic to their limit, ε0. How can such an ordering be constructed? —Keenan Pepper 19:46, 16 August 2006 (UTC)
 * First, partition the naturals into infinitely many infinite pieces. On the first piece, put your ordering for &omega;. On the second piece, put your ordering for &omega;&omega;. And so on. Now string them all together. --Trovatore 19:51, 16 August 2006 (UTC)
 * Whoa. I guess that works for any countable limit ordinal. Thanks! —Keenan Pepper 21:16, 16 August 2006 (UTC)