trying to find a pattern may be dangerous

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hk
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trying to find a pattern may be dangerous

Post by hk » Wed Apr 05, 2006 6:31 pm

In a school class a problem was stated.
A pupil solved this problem by drawing and counting for small cases and found: 1,2,4,8,16 and then reasoned the next number would be 32, which was wrong.
What was the problem stated?

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Alvaro
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Post by Alvaro » Wed Apr 05, 2006 7:20 pm

If I had to take a guess, I would say "In how many parts can the 4-dimensional space be disected using n hyperplanes?"

Another option is "if your legs are long enough that you can go upto 4 steps at a time, in how many different ways can you go up a flight of n steps?"

Just as the first 5 terms don't determine the 6th, the first 6 terms don't determine the sequence. So the question could have been pretty much anything.

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Post by hk » Wed Apr 05, 2006 7:33 pm

well, if you found that hyperplane thing, you can also find what problem a highschool kid can be tackling drawing. (it's the same sloane entry)
This is also a very famous one

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Alvaro
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Post by Alvaro » Wed Apr 05, 2006 7:42 pm

hk wrote:well, if you found that hyperplane thing, you can also find what problem a highschool kid can be tackling drawing. (it's the same sloane entry)
This is also a very famous one
I didn't "find" anything. I happen to "know" some of these things, although I can't think of the alternative problem that produces the same sequence. Ok, I just looked it up. So the problem you had in mind was this chords-dividing-a-circle thing.

However, I don't see why a highschool kid couldn't tackle the staircase problem by drawing.

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Post by hk » Wed Apr 05, 2006 7:49 pm

Last edited by hk on Wed Apr 05, 2006 7:52 pm, edited 1 time in total.

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Post by jdrandall123 » Wed Apr 05, 2006 7:49 pm

A better guess at a high-school problem.


Number of divisors of n! The answer should be 30, not 32.

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hk
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Post by hk » Wed Apr 05, 2006 7:53 pm

also a fine one. But drawing?
Some nice ideas for a lesson, I think

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Post by euler » Wed Apr 05, 2006 10:32 pm

I guess it would be twisting the wording of the puzzle slightly to say that the "drawing" was taking numbered discs at random from a bag, but I thought people might be interested in this example of an unexpected next value...

Consider the number of different products that can be taken from the set of consecutive natural numbers, {1,2,3,...,n}.

n=1: 1 (1)
n=2: 1,2 (2)
n=3: 1,2,3,6 (4)
n=4: 1,2,3,4,6,8,12,24 (8)
n=5: 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 (16)

If you count carefully you should get 26 for n=6.

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Re:

Post by kenbrooker » Wed Apr 11, 2018 2:21 am

Alvaro wrote:
Wed Apr 05, 2006 7:20 pm
Another option is "if your legs are long enough that you can go upto 4 steps at a time, in how many different ways can you go up a flight of n steps?"
What happened to your 3 steps (not in the riddle)?

And Euler's immediately preceding post is
Indeed interesting...
"Good Judgment comes from Experience;
Experience comes from Bad Judgment
..."

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Re: trying to find a pattern may be dangerous

Post by hk » Wed Apr 11, 2018 11:49 am

The last time Alvaro visited this forum was Fri, 14 Dec 2012 23:05:12.
Probably got lost in some hyperplane maze. :lol:
So I don't think he will elaborate on his flight climbing thing.
Image

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Re: trying to find a pattern may be dangerous

Post by kenbrooker » Wed Apr 11, 2018 4:22 pm

My "secret" intention was to facilitate helping people who joined PE.chat after 2006 (perhaps the majority?) enjoy your good/entertaining point that "trying to find a pattern may be dangerous" and, to enjoy Mr Euler's interesting, to me, reply (or Maybe I "think" too much, which also may be dangerous : )
"Good Judgment comes from Experience;
Experience comes from Bad Judgment
..."

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Re: trying to find a pattern may be dangerous

Post by hk » Wed Apr 11, 2018 7:04 pm

I may be wrong but in my opinion Alvaro pretty much killed the thread with his gruff response.
Image

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Re: trying to find a pattern may be dangerous

Post by kenbrooker » Wed Apr 11, 2018 9:32 pm

NOT TO DISAGREE WITH YOU hk but I, for one, went on to enjoy your two links, and jdrandall123's and euler's thoughts, though indeed it would be hard to do a "drawing" for
a High Schooler (or maybe even for a Rocket Scientist...)...

I hope you won't give up on alerting us to any other idiosyncrasies, especially
considering my quote below...
"Good Judgment comes from Experience;
Experience comes from Bad Judgment
..."

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