Ancient Brain Teaser.

[elfs]

Yamaarashi-chan was bugging me last night with numerical sequences and "what is the next number". They were mostly simple things: multiples of n, although one of them was the classic Fibonacci sequence. So I gave her a hard one: of the digits 0 through 9, you're given the following sequence: 0,2,3,6,7,1,9. In what order do the last three digits go, and why?

Comments

[kitsap_charles]

4, 5, 8.

Reverse alphabetical order of the English words for the numerals.

Reminds me of a classic about sequencing every number alphabetically by its (English) name. Even though there are an infinite number of number-names, you can always determine which one will be last.

[kenshardik]

As a former mathematician, all I can say is:

EVIL! EVIL!

Ow, my brain hurts.

[srmalloy.livejournal.com]

Reminds me of the day, back in college, when I got out of ever getting called to the board to do proofs in one class. There were three of us who got to go to the chalkboards and prove various theorems. Mine was that the summation of the integers from 1 to N was N*(N+1)/2. And I know that the professor expected a mathematical proof. But that wasn't what I gave him. I walked up to the board, drew this diagram:

     O\O O O O O
       \
     O O\O O O O
         \
     O O O\O O O . . .
           \
     O O O O\O O
             \
     O O O O O\O
         .
         .
         .

then wrote 'Q.E.D.' underneath, and sat down. The professor was annoyed; I didn't do it 'right'. The proof is valid, though, so what he decided to do was send me back up to prove that the sum of the cubes of the first N integers was N^2*(N+1)^2/4. Now, if you're paying attention, that's the square of the formula I got for the first proof. So I walked up to the chalkboard, drew the diagram to the right, wrote 'Q.E.D.' underneath it, and sat back down again. The professor snapped his pencil. I'd short-circuited the proof process again, and again with a valid proof. And so, for the rest of the semester, I didn't have to worry about getting called up to do problems at the board... I was glad that one of my classmates had been given the formula for the sum of the squares of the first N integers to prove; the geometric proof for that one is a lot less clean.

[katybeth]

Got it. That's a nice one. I'd seen the inverse before, but not that variation.

[acelightning.livejournal.com]

[(Anonymous)]

Agreed, that requires knowledge outside of the problem that the Solver might not know. Of course for me I began having serious problems starting with fractions and my math career ground to a halt a matrixes. Every time I watched someone solve one of those it required a leap of logistical faith to move from one point to another, and I could never reproduce that. Oh well they can keep their fancy math, I can draw pictures of naked ladies.
-D

[acelightning.livejournal.com]

[(Anonymous)]

You win!
-D

[acelightning.livejournal.com]

[http://users.livejournal.com/_candide_/]

Actually, that's now the (6). The (4) became an express line and runs directly from 14th St.-Union Square to Grand Central, 42nd St.

(Gee, guess what I ride every day? :wink:)

[acelightning.livejournal.com]