Are you smarter than the 6th-grade MathCounts champion?
The prestigious Lockheed Martin MATHCOUNTS National Competition took place yesterday.
You don’t get there by learning Everyday Math crap.
It’s the real deal.
The winner of the individual contest was an 11-year-old 6th-grader from Bellevue, Washington, Darryl Wu.
Here was the winning question. Can you solve it?
And, oh, by the way, the question was timed. Darryl came up with the answer in less than 45 seconds.
Question: A set of distinct positive integers has a total of 11 digits, and all the digits are ones. What is the smallest possible sum of the integers in the set?
NO PEEKING at the answer, which is on the MATHCOUNTS website (update: or right here from commenter DougT, who clocked in with the answer first at 9:31pm Eastern).
And as my math teachers always told me: Show your work.
P.S. If you don’t even understand the question, welcome to the club!
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Ok, people, 45 seconds is up! Chop, chop.
Something positive for a change, Michelle. Thank you.
I got 11117, not sure if my logic worked… I’m not sure where to look on mathcounts. I’m guessing it meant ‘11 digits, each number positive, whole, and different.’ I’m probably way off. Took me a minute and a half…
I was told there would be no math.
Sorry added up tallies instead of totals…in other words I messed up my own logic. By my logic, it should be 11238 (hopefully, it’s been a long day).
No, no, exitus. You forgot to carry the 4.
The answer is 42. At least that’s what Deep Thought told me.
1+11+111+11,111=11,234
Took about two minutes to figure out what they meant.
LOL Mookie.
Seriously…is it time for recess yet?
I know! The 57 States of America!
Hat’s off to the kid. I understood the question but still screwed it up.
Speaking of 1’s and math,
Did you know that 1 in 10 don’t understand binary?
That was funny, Mixer14, but about 1/2 of us won’t get it.
Nigel Tufnel: The numbers all go to eleven. Look, right across the board, eleven, eleven, eleven and…
Marty DiBergi: Oh, I see. And most amps go up to ten?
Nigel Tufnel: Exactly.
…
Marty DiBergi: Why don’t you just make ten louder and make ten be the top number and make that a little louder?
Nigel Tufnel: [pause] These go to eleven.
Cannot find the answer on the website either, but I suspect since the question said all the digits are 1, but did not say positive or negative, my guess is 1.
Question clearly says positive, so as we used to make the new scouts chant the secret indian mantra: “Oh Wah Ta Id Eeaht Iam”
D’oh. Now, I get it. Thanks, Doug. When it said “ones,” I interpreted that to mean single digits.
English majors…
Everday Math major at Oberlin?
Har!
This is why I was (and am) an English major.
But - in all honesty - I think the answer is 11. “Positive integers” is just another way of saying “positive numbers”. Since they’re all single digits and there are 11 integers, the minimum is they could be is 1. 11×1 = 11.
Now let me see if I’m correct…
No, I wasn’t.
I’ll stick to writing, thankyouverymuch.
Yeah, well…well…I scored 98% playing Slow Ride on Guitar Hero III this morning! Take that, Darryl!
I don’t know I’ll take a completely retarded guess that won’t take more than 3 seconds:
{1,1,1,1,1,1,1,1,1,1,1}
1+1+1+1+1+1+1+1+1+1+1= 11
Mixer14, I have the perfect t-shirt for you.
Here!
Sorry that i’m not willing to play the math game tonight…I’ve spent all day performing calculations assessing risk with investments for a 400 level Economics class I’m taking…I come onto Michelle’s blog to take a study break , and what do I see-a math test!
This is evil Michelle!
DougT is the winner.
That is a great t-shirt and funny site. I might get a few gifts for my colleagues from there.
Can’t Mr Malkin tackle these elementary math problems? (I kid with the elementary, these children have some precious logical minds.)
*sits in a puddle of his own drool*
Michelle: LOL !!!
The left ot the right half?
Wow, and I’m an engineer from a top ten school… I am humbled this fine evening.
Darryl Wu is impressively precocious.
okay I lifted weights to get my blood circulating….yes the set would be 1,11,111,11111 ….eleven total digits and each didgit equal to “1″ add them up and there is 11,111 plus 123 which =11,234.
That is correct.
Ms. Malkin,
Will you do my homework?
Question: A set of distinct states has a total of 210 and 128 delegates, none of which will be seated at the convention. What is the smallest possible sum protests and money needed to seat the delegates?
Can the Democrats be as smart as the 6th-grade MathCounts champion?
Paging Darryl Wu, Paging Darryl Wu !
I’m bad at permutations, I’m assuming the rule is the elements of the set cannot be repeated and must maintain a sequence.
OK, now I get it.
It only took me 45 minutes…
And on this same page is the 20something bimbo Aliza Shvarts. I think the 11 year old math wiz would be a better candidate for Yale. Oh, never mind . . . . Darryl Wu is too bright for Yale.
Mixer 14
It will be $338×2 ….The reason is that Democrats will fight to the death for principle in Denver while their replacements pick up the remains and choose a warm Amoeba as President…something racially, sexually, politically neutral who will do George Soros’s bidding and make Juan Hernandez happy as he strokes his beard.
No sequence necessary, just distinct elements in the set. No repeats.
{1, 11, 111, 11111} is the set. All ones. Total of 11 digits. These are the numbers that create the smallest sum.
Other sets would be {111111, 11111} or {1111, 11111, 11} etc. But all of those sets would have a greater sum than the first set.
My problem, when I first read it, was confusing the word “ones” for a place value rather than a numeral. I think MM had the same issue.
I would of tried the math, but I spent the evening figuring out where to put my last few months of retirement savings. Energy ETF, here I come!
Cute.
.
But I thought we were going to count STATES!
Thats two (2) CP witches, 169 Drachma, and three (3) very long pews.
45 seconds? Is it too late to substitute Daryl Wu for McCain?
Wow…I actually got it. I’m totally stunned, I spent most of high school and college on the verge of failing my math classes.
Bob1234,
How can you ask an American of Quality such as Darryl Wu to run for office?!
That would invoke prejudice against the Quantitatively-Challenged!!
Haven’t read all the commentary yet. Been away from the computer a lot of today… I was on the right track “distinct positive integers” is the first clue - all the numbers are different, there are no negatives, and the numbers are all whole numbers (no fractions/decimals). I started with 1+11+111+1111 and was like “hey, that doesn’t work”. My brain is tired right now, so I just looked at Doug’s answer and did a “DOH!” to myself. I’d've figured it out eventually… And a “set” is just a group. Although I’ve always been good at math (5 years worth in 4 years of high school), I was rusty on terminology until I took the “teaching math in elementary” class while working on my M.Ed. Can’t think how to break down “digit” - it’s just a “number” (but not really…)
But in Binary?
The Answer to everything is:
101010
How… interesting…
Ehh… I still don’t get it. A math genius I am not, even though the respect I have for those who are mathematically inclined is ENORMOUS.
I’m also quite envious.
Took me a couple of minutes. I did it that quick because (coincidentally) this is related to a common kakuro combination (kakuro is a sudoku variant). The only way to get a total of 11 from 4 of the digits 1-9 is 1+2+3+5.
You can’t take 3 from 2, 2 is less than three, so you look at the 4 in the 8s place…
The shame is how easy this question really is. I think it is the wording that might trip most people up, as most have not encountered sets in years. But basic set theory should be taught to middle schoolers, and it should not even be the most advanced math they know at that point. Though, I might be a little biased as I was always ahead of my class in math anyway.
Why should I care? I bet I could beat up Darryl Wu.
Hooray for New Math…
I got it but not anywhere close to forty-five seconds. I am blaming it on being out of school for thirty years and not having to think along the same lines. All that aside, it is nice to see that real math is still being taught somewhere.
As for the Binary Romeo, I never did like the book or the movie. I know I am not alone but definitely in the minority there. Still, it just never interested me like it did many people.
And now, ladies and gentlemen, a math lesson from a distinguished professor - Prof. Tom Lehrer - and pay attention to the lip syncher at your own risk.
http://www.youtube.com/watch?v=tx5KDyvlG3Q
As they used to say in the engine room, “What do you want it to be?”
Gone all day and just got to check the site from out west …
Very straightforward problem actually but still impressive for an 11 year-old sixth grader to get it quickly.
To those still not sure of the logic involved to determine the “integers” to be added it lays out like this.
By definition an “integer” is a whole number, which can include “zero” and can be positive or negative.
A set is a group of such numbers with some sort of expressed relationship, in this case they consist of only combinations of the numeral “1″.
The problem stated “positive” integers so that immediately ruled out negative numbers and “zero”.
The stated fact that all the integers were “ones” made the first three positive integers obvious as “1″, “11″, and “111″ because the stated goal of the problem was to find the lowest sum for the integers. This used 6 of the 11 digits available in the problem.
One would normally expect the next integer to be “1111″, however the problem stated that the integers were “distinct” and using “1111″ would have left a single “1″ for the last integer. Since we had already used the integer “1″ that eliminated “1111″ from use because we would now have two integers of “1″ in the set violating the “distinct” guideline. This leaves the last integer as “11111″ by default.
Never liked Binary, although in the computer industry I still have to use it on occasion … but I also have to deal with Octal, HexaDecimal and Metric systems on a regular basis as well.
Sorry I missed the fun when it started on this one.
I got it in 1 minute. Only 4 hours late.
DesertLover~
You gave a much more thorough explanation than I did…
Could that be one well trained Marine marksman calmly pulling the trigger of his rifle in a highly disciplined manner despite the fact that he is in an intense firefight?
11 shots, 11 kills.
I could be wrong thought.
On May 11th, 2008 at 1:17 am, DesertLover said:
DesertLover,
I love people like you. Thanks for your input.
I still like the number 11.
Semper Fi
Well I think it was poorly worded.
BTW, where’s the “Math Prof” who usually trolls through…
Well no - 11 digits would require him to use a toe in addition to all ten fingers on the trigger. Wait - you said Marine - then the answer is yes.
I didn’t really understand the question before Desertlover explained it.
Hence why I leave maths in the capabke hands of professionals, 6th graders, and xkcd.
Not surprising that many teachers wouldn’t be able to do this; after all, the President of the UFT, Randi Weingarten could not add 1/4 and 1/3 in her head (NYT, 12/28/2006, NYT Region, David M. Herszenhorn).
Now I get it, and it does make sense to me.
God invented numbers and math to irritate me.
What’s an integer? Isn’t that what the civil rights marches were all about?
I coached a math counts team some years ago. We (the team and me) made it to the state championships but not the nationals. Of my two top kids, one just graduated Harvard as a math major and the other is a senior at Yale — also math major. The kids were amazing.
The cutest thing I saw was one of my kids who had a speech impediment and talked very slowly. He was at the podium and got the question “What is the largest integer less than 10,000 that is divisible by 12?” He answered immediately but slowly: “Nine fousan, . . . nine hundwed … and nindy six!” which is the right answer.
Off topic:
Happy Mother’s Day Michelle and to all your readers and commenters.
Z
I don’t do no stinkin math…..
“My problem, when I first read it, was confusing the word “ones” for a place value rather than a numeral. I think MM had the same issue.”
and that is the problem that I have with math problems. They are written for mathematicians NOT ordinary folks. A mathematically-trained individual interprets the term “ones” one way, while we ordinary iggerant folks interpret it another way.
In my profession I deal with folks from the IT side of the house and folks from the business side of the house. The first thing I try to do in meetings is make sure that we understand what certain terms we will be using mean. It never ceases to amaze how far apart the meanings of certain words are.
Oh, this is so sad. The answer is, in fact, 42. Deep Thought was right. In binary:
1+11+111+11111=101010
and 101010 is, in fact, 42.
1 to the 1111111111th power = 1
It’s amazing a 6th grader could figure that out in 45 seconds.
CAn I borrow a piece of paper?
LOL, ram…
I work in IT, but I am one of the few I’ve met who do not like math. I never found a huge need for it as a SysAdmin. I do more project management now, and the only math I handle is simple accounting and budgeting. Thank G-d for spreadsheets to do the math for me.
I re-read the “fuzzy math” thread from November 2007 and I remember my struggles with math all the way through college. Only when I got to college, did I find someone who could teach me math. To my amazement I did well in algebra. With the aide of a great tutor I passed the required pre-calculus and calculus classes.
When my fiancee’ and I get married and have kids. I live in fear of having them ask for help with math. Neither of us are any good at it.
Mooseman
I forgot to mention that binary conversion and hexadecimal conversion were some of the hardest math I struggled with and continue to struggle with….
Romeo: Thanks for the fish!
skey … You folks are correct had the problem stated that the values were binary and the result was to be expressed in binary (base-2)
BTW … Decimal (base-10) 11234 expressed in binary (base-2) is 0010101111100010 and expressed in hexadecimal (base-16) it is 2BE2
Mooseman
You might want to check out this link:
Math Calculators and Converters
May make life easier for you …
Hi DesertLover,
I’ve got various networking calculators on my work computer. Unfortunately, the Cisco exams don’t allow you to use them
When my co-workers get excited about math equations, and it does happen. I usually say “It was my understanding there would be no math during the debate”. Classic SNL
Mooseman
Mooseman
I hear ya … just trying to help out … that is a very complete math formulae site …
He probably doesn’t think it’s fair that a problem like this exists. It justs serves to harm the self esteem of the less able students.
Desert Lover,
You’re a good man in a storm. It was remiss of me not to thank you for the link.
I apologize.
Mooseman
I’ve gone thru 2 erasers, now what comes after the 1?
Mooseman … no apology needed … but if you check the link let me know what you think of it … came across it a while back and thought it was pretty complete for a free site …
DesertLover, overall, great explanation. Just one nit to pick concerning the term distinct: if the question had not specified distinct, the answer would have been 11, not 1234.
kylos
Agree … there are a multitude of variations in wording that would present lots of possible “ifs” in the stated problem which would affect the outcome …
I was just trying to help clarify for some here that seemed, from their comments, to still be confused in their understanding of the problem even though they had seen the answer.
My attempt at explanation was strictly based on the problem as it was stated.
It only took me about 20 seconds
…to scroll down and find DougT’s answer
Here’s what the answer probably is:
You have a collection of “integers” (whole numbers — no fractions or decimals). One number in your collection should be 1. If it’s not, you can make the sum smaller by changing one of the numbers to 1.
Now you have 10 digits left. The next smallest number allowed is 11, so you must use it. Otherwise again you could make the sum smaller by swapping out something for 11. Now you’ve used 1 digits and have 8 to go. You must use 111 (5 to go), then 11111 (the last five digits in one number). It seems surprising to have to use such a big number in the end. If you tried, say, 1111, you would have use only ten digits and have to use the remaining single digit. But that one can make only 1 and you’ve already used that.
The sum is 1 + 11 + 111 + 11111 = 11234.
This is not a terribly hard problem. I would expect the best kids I coached to be able to get it. These kids see lines of reasoning like this almost instantly.
Also, they practice a lot. The problem might seem vague, but if you’ve done dozens like it in practice, you know exactly what it means.
I see no harm in kids doing contests like this. The kids I coached loved it. But don’t mistake it for real math education, any more than you mistake spelling bees for real English.
This discussion is not helping my kids.
That is pretty damn amazing.
Thanks, all for an entertaining thread. I confess that I forgot the mathematical definition of “distinct” and had eleven ones, to add up to 11. (Liberal arts major). Once I realized that I couldn’t repeat numbers, the right answer made sense.
And thanks for the “New Math” song reference. And the binary t-shirt–I may have to send that link to computer programming friends of mine.
I’m sour.
I don’t like the use of the word distinct. I think they should have stated, “a set of unique positive integers…”
Couldn’t I argue that 1 and 1 are two distinct integers? They may not be distinct from each other, but…nah…I guess not. Math isn’t my problem - vocabulary is!!!
I like the binary answer!!! The questioner didn’t say “in base ten.” However, the rules are probably to assume base 10 unless otherwise stated.
Excellent post, Michelle.
This will blow you away…
Add all the digits that are in the answer…
11,234 = 11
blah, I got it in 15 seconds… but I’m late to the party =\
leepro …
nicely done … hadn’t taken time to look further like that …
Does the total change if you take global warming into account?
I understood the question correctly, but got the answer wrong because I rushed it.
I went with the set being {1111, 11111, 111111}, which leads to an answer of 123333.
Word problems can confusing to someone who has done them in a while, or was never taught the math terms. My teachers usually referred to the “ones” column as the “units” column for clarity. And most of these specialized math terms are for exactly that reason: clarity and precision.
The majority of my college professors were from the Math & Computer Science Department at St. Joseph’s University, and I took all the way up to Calculus III & Linear Algebra. I sucked at, but I got a good grounding in the terminology.
MM, thanks for keeping the heat up on Everyday Math.
In my view, that instructional program has done more damage to students’ acquisition of basic math skills than is imaginable.
For example, in 1998 - at the insistence of our new principal, the elementary school where I was teaching 7th and 8th grade math at that time implemented the program and went from a ranking of “High Performing” to “Academically Deficient” on our state’s testing system, within the space of two test cycles.
My chief complaint with the program is that although it attempts to deliver sound mathematical theory and alleviate students’ math anxiety, it utilizes a meta-cognitive/self-awareness approach that is too introspective to properly instruct math reasoning strategies and often fails to go beyond the introductory phase in teaching number concepts and manipulation skills.
I hope your continued exposure of this failed math program serves to caution parents and schools across the nation against adopting Everyday Math into the curriculum of their schools - if they want their students to learn real math.
Now lgm, did you allow your student to move forward, or did he have to wait till ALL students got it? After all no child is to be left behind
Skey,
LOL. I see you’ve read “The Hitchhiker’s Guide to The Galaxy.”
errah, I cut class that day unfortunately it was drivers ed, errah.
I get 2,047 in Binary.