WWTBAM Bored

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?

Let's just say it took me much longer that 45 seconds just to figure out what the question meant.

Took me more than 45 seconds to figure it out (what the question meant) as well...

Spoiler

...but the answer is 11,414.

1 + 11 + 111 + 11,111

Jeemie wrote:Took me more than 45 seconds to figure it out (what the question meant) as well...

Spoiler

...but the answer is 11,414.

1 + 11 + 111 + 11,111

Spoiler

I think your problem is correct, but your addition is a bit off.

I come up with 11,234. Took me about 20 seconds because I had to fire up my calculator.

Thing is, for math junkies, there's an algorithm for this type of problem that allows you to do it in less time. Sort of like knowing in advance that each FF question is going to contain 4 unique integers, and also being able to rule out certain combinations (like 1234, for instance). One of the many nice things about mathematics (if you're good at it) is that it's one of the few arenas where extreme youth can be a benefit, rather than a disadvantage.

I dare say this 11-year-old would be better at math skills than many, if not most, university professors.

TheCalvinator24 wrote:

Jeemie wrote:Took me more than 45 seconds to figure it out (what the question meant) as well...

Spoiler

...but the answer is 11,414.

1 + 11 + 111 + 11,111

Spoiler

I think your problem is correct, but your addition is a bit off.

Holy crap!

That's what I get for doing it by hand!

Interesting.

Spoiler

the age of the prize-winning solver

is the answer, according to me. Depends on the meaning of "distinct" which I interpret as "identifiable", not "different".

If not, then to get to 11 digits, 5,3,2,1 is the smallest.
11111 + 111 = 11222 + 11 = 11233 + 1 = 11234.

I didn't time myself, but it took me less than 45 seconds. It seems more like a logic problem than a math problem.

Were paper and pencil allowed?

Spoiler

If so, the answer is 11234.

Edit: OK, my first answer wasn't optimised, then I edited it once but had the number of digits wrong. Now I think I'm right, but I didn't make the 45 second cut-off.

Not really that hard a problem. I didn't specifically time myself but started working on it the moment I saw it. Maybe it took 10 to 15 seconds.

You guys are so cute.

Not sure I am smarter, at least when it comes to math, but I got this one without that much difficulty and in less than 45 seconds from the safety and comfort of the Lazyboy.