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20 iterations

20 iterations

Posers and Puzzles

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Start with four numbers:
a b c d

Fill in subsequent rows by taking the absolute value of the number above minus the one above and to the right:
|a-b| |b-c| |c-d| |d-a| (d has nothing to the right, so we 'wrap around' and use a)

The challenge is: Find numbers a, b, c, and d that yield 20 rows where at least one number on each row is not zero. (not counting the initial row)

Example:

If we start with 1, 2, 3, 4, we get:
1 1 1 3
0 0 2 2
0 2 0 2
2 2 2 2
0 0 0 0

This counts as 4 iterations.

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Originally posted by SwissGambit
Start with four numbers:
a b c d

Fill in subsequent rows by taking the absolute value of the number above minus the one above and to the right:
|a-b| |b-c| |c-d| |d-a| (d has nothing to the right, so we 'wrap around' and use a)

The challenge is: [b]Find numbers a, b, c, and d that yield 20 rows where at least one number on each row is not ...[text shortened]... 2, 3, 4, we get:
1 1 1 3
0 0 2 2
0 2 0 2
2 2 2 2
0 0 0 0

This counts as 4 iterations.
100, 3, 2, 1

?
did I understqnd the question right?

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Originally posted by agryson
100, 3, 2, 1

?
did I understqnd the question right?
Using those numbers, i get

100321
971199
960982
96989694
2222
0000

...which is only 4 iterations.

Order of operations is to subtract first, and then take the absolute value of that result.

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Originally posted by SwissGambit
Using those numbers, i get

100321
971199
960982
96989694
2222
0000

...which is only 4 iterations.

Order of operations is to subtract first, and then take the absolute value of that result.
hmm... ok, I'll work on it tomorrow,

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Originally posted by SwissGambit
[b]Start with four numbers:
a b c d
Spot the mistake?

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Originally posted by invigorate
Spot the mistake?
The mistake is tackling a problem like this without a basic knowledge of algebra.

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Originally posted by invigorate
Spot the mistake?
I don't. What is the mistake?

I like this problem! Really!
Now I have something to think about during boring meetings.

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The mistake is a b c and d are letters not numbers!!!

HA HA HA!

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Originally posted by Gastel
The mistake is a b c and d are letters not numbers!!!

HA HA HA!
Who says they are letters?
He says from the beginning: "Start with four numbers: a b c d"
If he says the symbols are numbers they are, believe me. They perhaps look like letters but they are in fact numbers.

Can you solve the equation 2x=4 not realizing that the x stands for a number?

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I think he was trying to be funny.

Trying.

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Originally posted by mtthw
I think he was trying to be funny.

Trying.
Who? invigorate or Gastel or both? Exactly the same kind of humour? Strange...

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a=pi
b=e
c=sqrt(2)
d=sqrt(3)

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Originally posted by David113
a=pi
b=e
c=sqrt(2)
d=sqrt(3)
Doesn't work! Hits zero in four iterations 🙂. Try it out.

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I spent some time trying to come up with a pattern that worked. No luck so far.

So went for the brute force approach 🙂. Best so far is [4910, 4163, 2789, 262], which gives the 20 iterations you wanted.

I'm sure there's a better way.

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Originally posted by David113
a=pi
b=e
c=sqrt(2)
d=sqrt(3)
Oops...the stipulation should allow only whole numbers.