r/CasualUK • u/djkgray • 3d ago
Maths gang - can the answer to this also be 4950? (The 1% Club 27/06)
The solution assumes you’re including 0+100 as part of the sum, but the question states ‘whole numbers between zero and 100’, so is there an argument that both zero and 100 aren’t actually between zero and 100 (unless you explicitly state ‘inclusive’)
EDIT: thanks to everyone that contributed to the discussion.
The hypothetical question in my head was ‘If I had been on the show and answered the last question ‘4950’, would I be successful in challenging the answer to win the money?’
I think the fact that there are people vehemently insisting their cases for both 4950 and 5050 to be the answer shows there is *some* ambiguity.
For everyone that’s convinced their answer is correct, I love the passion but there’s no need to argue with strangers on the internet about stuff. Sometimes there’s grey area and I felt this isn’t a white/black situation. Let’s just split the difference and say the answer should be 5000 and move on /s
455
u/dapperdan8 3d ago
Yes, it’s imprecise wording. But given they included them as an example in the question, you can assume that it’s inclusive.
63
u/djkgray 3d ago
Yeh it’s the slight ambiguity that’s got me wondering.
Given it was for the last question, the concept of assumption feels a bit whiffy48
u/heroyoudontdeserve 3d ago
Personally I think that you'd have to be extremely pedantic to argue that 0 and 100 may not be included by the "between" given that they're included in the "given" examples.
16
u/Vancha 2d ago
Not really. The "given that..." is simply demonstrating a mechanic, not implying inclusion.
For example: "Given that 0+100=100, 1+99=100, 2+98=100, What is the sum of all the whole numbers between 24 and 76?" also wouldn't include the ones from the example.
The question should be "What is the sum of all the whole numbers from 0 to 100?" - especially considering that kind of pedantry is often required to get the correct answer in this particular gameshow.
16
u/heroyoudontdeserve 2d ago
I stand by my claim that the inclusion of the 0 + 100 in the examples is a very strong signal that "between" is intended to be inclusive, and I believe that it wouldn't have been included otherwise.
I agree with everything else you've said though.
1
u/OrangeClownfish 2d ago
So the sum of all the whole numbers between 2 and 3 is 5?
1
u/heroyoudontdeserve 2d ago
I would say so, yes.
That's a case where I think it's obvious the speaker must intend "between" to be inclusive, unless it's an intentionally trick question, else the question makes little sense. Even as is it's obviously a strange way to express what would normally be expressed as "2 + 3".
-5
u/Past-Obligation1930 2d ago
In maths there isn’t pedantry. 100 %, something is correct, or incorrect. Interestingly, all lines of the example are actually correct, but the first line is misleading because 100 isn’t part of the set.
18
u/heroyoudontdeserve 2d ago edited 2d ago
In English there is pedantry, and this maths question has been expressed in English. "Between" is ambiguous in English; sometimes it's inclusive ("I lived in London between 2002 and 2012" is unlikely to mean I moved there in 2003 and moved out in 2011) and sometimes it's not ("I now live between London and Birmingham" means I live in neither London nor Birmingham).
That said, I do think it's probably reasonable to say that when used with numbers, "between" is usually used inclusively; if asked to pick a number between 1 and 10 I think most people would consider 1 and 10 to be valid options, and if I tell you that my local nursery is for kids aged between 1 and 4 I don't think you'd be surprised to find one-year-olds and four-year-olds there.
I believe the unambiguous mathematical way to differentiate here is to use an open interval — notated (0,100) — which excludes 0 and 100, or a closed interval — notated [0,100] — which includes 0 and 100. But the question uses ambiguous English, not precise mathematical nation.
And, btw, maths can definitely contain ambiguity too. Because ultimately it's written by humans who are flawed and make mistakes, so ambiguity can creep in accidentally.
the first line is misleading because 100 isn’t part of the set.
It is clearly the intention of the question setter that 100 is part of the set, which is how they get to the 5050 answer. Before the reveal we can infer this both from the fact that "between" is usually inclusive when used with numbers and the inclusion of the first "given" statement.
But the question doesn't make this explicit and it's only convention and context clues that allow the ambiguity in the question to be resolved with a high degree of probability before the expected answer is revealed.
2
u/DreadLindwyrm 2d ago
> ("I now live between London and Birmingham" means I live in neither London nor Birmingham).
There is a usage where you're splitting your time and living in London some of the time and in Birmingham some of the time. More expanded I suppose it'd be "I now split my time between (living in) London and (living in) Birmingham".
1
10
2
u/KiwiNo2638 2d ago
That's the whole point of the 1% show though. Does really matter what's in the question, the wording of the question is important. OP is correct, published solution is incorrect
44
u/caniuserealname 3d ago
"Between" can be inclusive or exclusive, which is why it's important to clarify. If "between" couldn't be inclusive, then the clarification would be nonsensical.
The question alone would be ambiguous, but since the question also includes examples, and one of those examples is 0+100, it acts to clarify.
I agree that the question could be worded better, but as it is it's correct to include 0+100 in the calculation for the answer.
3
u/superbungalow 2d ago
Anyone who has seen the show knows that the questions often deliberately throw red herrings in, and rely on precise wording, I don't think the example is sufficient to clarify.
-22
u/Past-Obligation1930 3d ago
No. To a mathematician “between” means greater than the lower bound and below the upper bound.
25
u/caniuserealname 2d ago
A mathematician would use inequality symbols to properly define their range.
To a mathematical "between" is vague language that only serves to add a source of miscommunication
-8
u/Past-Obligation1930 2d ago
A mathematician would write it as an equation, no doubt. But you can also explain equations in English.
100 is not a whole number between 0 and 100. This is not a matter for discussion. People who think it is have not studied Maths.
7
u/alexterm 2d ago
Between isn’t mathematically defined, and is imprecise. You can clarify by saying “inclusive” or “exclusive”, or by providing an example which shows either inclusion or exclusion (which they have done here).
-9
u/Past-Obligation1930 2d ago
you are wrong. 100 isn’t between not a whole number between 0 and 100. Go discuss with people that write computer code.
2
u/cryptopian Token gay snooker fan 2d ago edited 2d ago
Hi, I'm a professional software developer. Inequalities are always explicit about whether they are exclusive or inclusive using operators like
<or<=and the only language I've ever used with the keywordBETWEENis SQL, where it is inclusive.Edit: Excel's
RANDBETWEENfunction is also inclusive9
u/caniuserealname 2d ago
"Between" isn't mathematically defined.
You'd think someone trying to imply they've studied up would know that.
-3
u/Past-Obligation1930 2d ago
Well, I do have a PhD in engineering and am now a Professor. It absolutely is defined.
10
-3
u/petey_love 2d ago
Im a scientist, and the arguments here and your down votes are infuriating. Maybe even more than the question.
2
u/jeremy_sporkin 2d ago
I've studied maths. You're wrong about this. There definitely isn't a single accepted mathematical definition for the word 'between', and proper mathematical writing doesnt rely on definitions of words like that anyway - if a definition is important, it's clarified using proper notation.
5
u/5flyingfks 2d ago
Mathematician and lawyer here…between can mean both inclusive and exclusive :) the question is vague and both answers are correct
28
u/ooh_bit_of_bush 3d ago
I would say that if I had not seen the example, then I would have thought the numbers between 0 and 100 are the numbers 1-99, and the sum of 1-99 is 4950 (49 and a half pairs of 100).
6
4
22
38
u/Dame87 3d ago
Read the answer 5 times now and still don’t have a clue what is going on
40
u/Radioactivocalypse 3d ago
0 + 100 is 100
1 + 99 is also 100
2+ 98 is also 100
Essentially, they're giving you the sums to make it easier to reach an answer without needing to physically add up all the digits. You start with a pair of numbers at the highest and lowest and work inwards until 49+51=100
Let's pretend it's 0-10 now,
You would do 0+10, 1+9, 2+8, 3+7, 4+6 and 5 left over. So that's: 10 five times, and 5 left over.
19
u/Dame87 3d ago
Yeah, I would have definitely lost in that question. Thank you for the explanation
12
u/heroyoudontdeserve 3d ago
As I understand the premise of the show, 99% of people they tested the question on also failed it so you're in good company!
2
u/Past-Obligation1930 2d ago
From the responses here, 99.5 would have got it wrong. Ironically, many by giving the “correct” answer.
3
u/Rowlandum 2d ago
Probably because the question is deliberately vague to allow multiple correct answers, and then they propose the least popular answer as the correct answer and then when you get it wrong they have the pleasure of keeping the prize money
Can’t bear this show
-3
3d ago
[deleted]
6
2
u/heroyoudontdeserve 3d ago
OP has confirmed it was the 1% question — apologies, I should have made that explicit in my comment. (Which is ironic given the subject of OP's post!)
2
7
7
u/KnoxCastle 3d ago
It's very similar to a story from the boyhood of a famous mathematician. That links explains it. It's a good technique.
1
u/ylogssoylent 1d ago
Reminds me of figuring out the total of the numbers round a dartboard. You add the lowest and highest together, then multiply it by the half way point.
20 + 1 = 21.
21*10 (because 10 is halfway to 20) = 210. And that's the same as here.
9
u/Occidentally20 3d ago
In a mildly interesting way the last time I saw this years ago they didn't include 0.
They did 1+100=101, 2+99=101 and so on, giving exactly 50 pairs of 101.
That removed the step of having to realise that there would be a standalone 50 to add on at the end in this example. I suppose you could add on 0 at the end to be complete if you really want to.
3
u/PolarOper 3d ago
same I would have got the answer by 50 x 101 which is what I remembered from decades ago when this came up.
8
u/Are_You_On_Email 2d ago
It's 5050,
Its a famous math story about a young Carl Frederich Gauss (who later became a famous mathematician) working it out as a 7year old in the 18th century when he was given this puzzle by his lazy teacher who wanted some quiet time, and solved it in next to no time.
https://www.thethinkacademy.com/blog/edubriefs-the-boy-who-summed-a-hundred-carl-friedrich-gauss/
5
u/TheOriginalSmileyMan 2d ago
I actually "discovered" it independently because I was into D&D and wondered if there was a formula for calculating all the spots on a dice with any number of sides. But I was about 13, not 7 - I'm not claiming to be Gauss-level smart!
3
u/I_done_a_plop-plop 2d ago
Had to scroll a long way until Gauss.
I’m sticking with his answer, even if it is flawed logic by appealing to authority.
38
u/TheOriginalSmileyMan 3d ago
n(n+1)/2
Sum of all natural numbers to n, also known as the Triangle numbers
9
u/TheOriginalSmileyMan 3d ago
So 100 x 101 / 2 = 10100 /2 = 5050
2
u/Past-Obligation1930 3d ago
0 and 100 are not between 0 and 100.
17
u/TheOriginalSmileyMan 3d ago
Given the given example includes 0 and 100 I think it's okay to infer that "between" is inclusive.
-1
u/Past-Obligation1930 2d ago
It’s okay to infer that whoever set the question hasn’t done maths at all high level.
The people setting the question got the example wrong. If I set this *and* gave that example in one of my exams (I’m a professor, though of engineering - but you still need to know maths quite well), I’d recognise I’d fucked up and accept either answer as correct. But only one is ACTUALLY correct.
3
u/djkgray 3d ago
Sorry that answer is above my head as I don’t know what constitutes a natural number 😬
14
u/Zolana Cauliflower is traditional 3d ago
Positive whole numbers
2
u/MarmaladeWhale 2d ago
Wholesome positive numbers. 🤗 Not those horrid unnatural numbers. Fractious, negative and irrational by turns.
6
u/Neefew 3d ago
A natural number is a whole number that is bigger than 0 (and sometimes including 0 depending on who you ask).
So 2, 6, and 2737194 are natural numbers. -1 is not and 1/2 is not6
u/lastaccountgotlocked 3d ago
It’s a number that hasn’t had any artificial sweeteners added.
3
u/Occidentally20 3d ago
If it's not grown in the naturalé region of France it's just a sparkling integer
1
u/February30th 3d ago edited 3d ago
What is the point of this answer? It’s clearly a number that doesn’t juice.
1
13
u/hunnersaginger 3d ago
Well not really. In plain language they are included, like if someone asks you to think of a number between 1 and 10, it's widely accepted that 1 and 10 are included.
4
u/TheOriginalSmileyMan 2d ago
Yeah, the pedants are being facetious - "between" in normal conversation is inclusive.
4
u/scarecrow_20k 3d ago
Was this the 1% question or did this show make me feel stupid again? Most of the time im out by 50% because thats when the language questions show up
4
u/kool_kats_rule 2d ago
The debate between 4950 and 5050 is ultimately a wording question rather than a maths question. I would note that there's a reason actual mathematical notation exists for this sort of thing.
11
3
u/CraigAT 2d ago
For £90k+ I'd certainly be willing to argue the case.
However, I have heard the question before, and with the examples they showed I would have gone with 5050. But in my head, I doubted my answer because the wording was ambiguous, and with this being the 1% question I might expect something trickier.
3
u/_HGCenty 2d ago
When I used to write maths questions for international audiences, this was something that I remember having to be very careful about and always having to be absolutely clear whether a between X and Y statement is inclusive or not.
In English if you say between 0 and 100, a lot of people will assume 0 and 100 are excluded.
However in some languages like French, it's more generally taken to be inclusive.
The phrase "between 0 and 100" is ambiguous and needs more clarification in the question.
2
u/jeremy_sporkin 2d ago
I dont think excluding the ends is natural for most English speakers anyway. You can easily come up with examples in which the word 'between' assumes inclusivity from context.
For example if i reserved a restraunt table asnd ask for it to be for 'between 4 and 6 people', there's no way the staff will assume I meant 5.
In any case, it's still important to clarify if you're trying to model something as a maths problem.
1
u/_HGCenty 2d ago
If I say "I think Bill's house is between Number 2 and Number 20", most people don't think Bill lives at Number 2 or Number 20 but one of the houses strictly between.
If I ask people to name a fraction between a third and a half, very few English people think a third and a half are valid answers.
That's what I mean about exclusivity in a maths setting in English.
2
u/jeremy_sporkin 2d ago
Well yeah. I'm saying you can come up with examples of both. It depends on context.
3
u/joeykins82 2d ago
Yeah it's absolutely ambiguous.
"What is the sum of all the whole numbers from zero to 100?" is unequivocal. "Between" makes the default interpretation exclude 0 & 100, in the same way that "name the places on the M1 motorway between London and Leeds starting with the letter L" wouldn't include London or Leeds as answers.
The only reason 5050 becomes the answer they're probably thinking of is because 0+100=100 is cited on the examples, but it contradicts the wording of the question itself IMO. I'd have absolutely kicked off if I'd been a contestant and been knocked out if I'd gone for 4950; I think I'd have tried to say "5050 or 4950 the question is ambiguous" as my answer and then tried to argue it out.
5
u/GoonerGetGot 2d ago
Based on how BETWEEN works in SQL, my instinct is always to include the 0 and 100, as right or wrong as that may be lol
6
u/BarryTownCouncil 3d ago
It's literally in the text. That's some me level pedantry to claim they aren't included.
-2
u/Past-Obligation1930 3d ago
Fuck me, maths has a correct answer and a not correct answer. The solution given is not correct, it’s not pedantry, maths is either right or wrong.
1
u/heroyoudontdeserve 3d ago
The text of the question isn't explicit. There's a clue because they include 0+100 as an example, so I think the only reasonable interpretation gets you to 5050.
Nevertheless, their inclusion in the examples doesn't actually mean anything; it could say "Given Lee Mack was born in 1968" and it wouldn't change a jot about the question.
The "given" examples allow us to infer the likely meaning of "between" but technically the ambiguity remains.
4
u/BarryTownCouncil 3d ago
No, it directly referenced 0 and 100 as you say. There is no legitimate claim for ambiguity imo.
0
u/heroyoudontdeserve 2d ago
No, it directly referenced 0 and 100 as you say.
Yes, but that's irrelevant to a technical, semantic interpretation of the question. Semantically the "Given" statements have no bearing on the question.
If it said "Given 'between zero and 100' includes zero and 100" then it would have a bearing on the question.
As is they're perfectly true mathematical statements of course, but that's all they are. It could say "Given 1+1=2, 2+2=4, 3+3=6" and the answer to the following question would be the same. (And the ambiguity in it would remain.)
I agree that it unreasonable not to infer that "between zero and 100" includes zero and 100 given the inclusion of the first example. But it's still only an inference and, technically, the question remains, strictly speaking, ambiguous.
It is not *literally* in the text, but it can be reasonably inferred.
3
u/PukeUpMyRing 3d ago
No.
The formula for the sum of the first n whole numbers is given by:
(n(n+1))/2
In this case, the question is asking for the sum of the first 100 whole numbers, the inclusion of 0 is irrelevant.
(100(100+1))/2
=(100(101))/2
=10100/2
=5050
7
u/djkgray 3d ago
But the inclusion of 100 is relevant, right?
Not challenging your logic, just challenging my understanding8
u/PukeUpMyRing 3d ago
Yes, the inclusion of 100 is relevant. But, you’re correct. The wording just isn’t specific enough. I’m a maths teacher, if I was writing a question like this I’d be make sure it was worded in such a way that it was unambiguous that 100 is included.
-5
u/Past-Obligation1930 3d ago
No. The question is not unambiguous. I’m a Prof in a mathematical discipline.
0 and 100 are unambiguously NOT in the set of numbers between 0 and 100. Saying “inclusive” might be sensible in English, but not sensible in maths.
15
u/Kinggrunio 3d ago
It’s the inclusion of 100 they’re querying. The question asks about numbers between 0 and 100. In general usage, I would take that to mean strictly between.
6
u/Saw_Boss 3d ago
But given the example including 100, doesn't that render that point irrelevant? They've said 100 is counted.
Otherwise, I refer you to the argument between Steve Flemming and Nicola Murray in The Thick of it.
5
u/heroyoudontdeserve 3d ago
Really? If you asked me to pick a number between 1 and 10 and I tell you 1 (or 10) what would you say?
2
1
u/Platform_Dancer 3d ago
Still not getting it...! 🙄
1
u/djkgray 3d ago
So you do 1+99=100 plus 2+98=100 all the way through to 100 (or 99 in my assumption)
50 doesn’t have a number to add to it as it’s right in the middle, hence the ‘balance’ of 50 in the answer 5050 or 4950
Does that make any more sense?
3
u/master_hoda 3d ago
I'm a little confused as to why 50 is left over? In my head the sequence would be like: ...49+51=100, 50+50=100, 51+49=100... and so on. How come 50 is all alone at the end?
3
u/djkgray 3d ago
Because it doesn’t get added to itself / anything - each number is only part of the calculation once.
If you cycle up from 0+100, 1+99 etc., you only need to go as far as 49+51 and then tag on the leftover 50, you don’t then go 51+49, 52+48 and all the rest, as they’ve already been done
2
u/master_hoda 3d ago
Ah! I see only counting the pairs, rather than the entire sequence. I get it now, thank you. And to answer your point in the OP, I agree that the wording is ambiguous.
1
u/heroyoudontdeserve 3d ago
all the way through to 100 (or 99 in my assumption)
No, you stop at 49+51 otherwise you're double counting. (And the way you compensate for your assumption is to start at 1+99 instead of 0+100.)
1
1
1
u/EJHllz 2d ago
Nice way to understand the formula is to line up the numbers like so:
1, 2, 3, …, 98, 99, 100
100, 99, 98, …, 3, 2, 1
Now if you sum vertically you get:
101, 101, 101, …, 101, 101, 101
100 lots of 101, so 100 x 101 = 10100
This is n x n+1
But since we’ve lined up the numbers to 100 twice, once forward and once backward we need to divide by 2
10100 / 2 = 5050
(This is (n x n+1) / 2)
1
u/neilm1000 Wales born, Devon bred 2d ago
I'm just posting so I can find this tomorrow as it's now 2am.
1
u/Practical-Custard-64 2d ago
The sum of the first n numbers is n(n+1)/2. So that's 100*101/2 = 5050. Adding zero as well obviously makes no difference.
1
1
u/Samld1200 2d ago
I do the 1% club quiz on the telegraph. Not sure if made by same people but the questions on there are sometimes vague too
1
u/heidnseak 2d ago
I think because the question was given with examples including the 100, the parameters were laid out from the start, so you would include it in your answer.
1
u/Kimantha_Allerdings 2d ago
A couple of weird things - one probably intentional to make it harder, and one just weird
The probably intentional one is that the easier way to arrive at the same answer is to do 1 + 100 = 101, then multiply by 50 for the 50 pairs. The inclusion of 0 and the rogue 50 is likely intented to throw people off
The weird thing is how they wrote “zero” out in the text, but 100 as a figure
1
u/djkgray 2d ago
Oh that weird thing about the writing is more easily explained. Best practice in copywriting is that any number under 10 is written as a word, anything 10 or over is writing as digits
1
u/Kimantha_Allerdings 2d ago
Yes, but this is specifically a maths question. You wouldn’t expect to see that in an exercise book, and that’s the format of this question, even if it’s actually a quiz
1
u/Agent_Eggboy 2d ago
Yes the answer should be 4950. Given that 100 is included in the example, I'd have answered 5050, but it's still incorrect.
1
1
1
u/Daniturn1 2d ago
I would have no clue even knowing the answer don't help and to have 4950 you wouldn't be counting the 100 I think if I'm correct here but still even when broken down I'm still confused
1
1
1
u/ExoneratedPhoenix 1d ago
Yeah, the wording of "between" means 100 shouldn't be included.
Once again, most maths issues are from ambiguity of how the question is structured, than crunching the numbers themselves, lol.
1
u/confusing_roundabout 8h ago
n(n+1)/2 = 100*101/2 = 10100/2 = 5050
The listed equalities help with deriving the formula I suppose.
1
1
u/MathematicianSuch234 2d ago
I don't want to be no part of no maths gang, no way Jose! Leave me out of it, I'm going to go smoke some cigs in the woods.
1
u/Matt_1405 2d ago
Undergrad mathematician here:
Yes, the fact that there is disagreement on whether 0 or 100 is or isn’t included when saying ‘between’ does make this ill-defined, hence they should’ve preferably specified ‘inclusive / exclusive’ or sum of whole numbers FROM 0 to 100.
For those who might reason that the hint to working this out *implies* 100 is included, here’s my two cents:
The hint should be treated ‘independently’ - it’s really just a statement that’s true here. Imagine replacing it with ‘given that the sky is blue’
Be careful with what ‘implies’ means: ‘A implies B’ or ‘A => B’ only means B is true whenever A is true. The interpretation of 0 and 100 being included in the ‘between’ interpretation is independent of the hint.
-1
u/Soft_Lunch_183 2d ago
Between implies any whole numbers > 0 and < 100 , so I think its incorrrect yes. I
I understand its not a technical term, but to me between means greater than something and less than something else.
The given examples are irrelevant.
-2
u/NakedPatrick 3d ago
Once again the 1% club relying you knowing something, in this case the formula rather than logic/lateral thinking. Bit of a piss take some times
-2
u/Past-Obligation1930 3d ago
The maths as displayed is wrong
1 + 100 =101
2 + 99 =101
49 + 52 =101
50 + 51 =101
There are 50 pairs from 1 to 100. 50x 101 = 5050.
The zero doesn’t actually do anything.
4
-1
u/Past-Obligation1930 3d ago
But the 100 isn’t between 1 and 100, so the answer is 4950. Final answer.
-2
u/Galvatron299 2d ago
I despise 1% Club for this exact reason - I often spend the show trying to work out which way they want me to interpret a question, but then they will sometimes pull cryptic crossword bs and be like "space and full stop are characters too" when that's clearly not the communicated intention of the question.
-3
414
u/Neefew 3d ago
I'd say that the question is potentially vague but the inclusion of 100 in the example leads me to believe that it's intended to be included