bonanova
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Posts posted by bonanova
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Do the cuts have to be straight lines?
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OK. It looks like what you do isThere are 4 balls marked as "A", "B", "C" and "D" in the order. So, randomly draw one out and then put it back to thenext draw position. For example,
ABCD -> 3 ©
CABD -> 3 (B)
BACD -> 4 (D)
DACB -> 2 (A)
So, the question is, how to calculate the final stage with a given draw sequence with minimum draw simulation?
[1] remove a ball at random
[2] re-arrange the other balls into their original order [e.g. ACD in line 3] but ... not ACB in the last line. I don't get that part.
[3] replace the removed ball at the beginning [left end] of the line.
OK now what are you asking? Can you rephrase it or give an example? Thanks.
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Loosely, perhaps, but not precisely:a : the father's age.b : the son's age.
so, it says:
1.a+b = 66
2.a = kb (k is a constant)
put second statement to first.
=> b = 66/((k+1))
since it doesn't say k needs to be Nature number.
therefore, b can be any number in between 0 to 50.
PS:
1. It is possible that the father is youger than the son. For example,
a man married with a woman who has a son and the son is older than the man.
2. At least, the father needs to be older enough to get married.
[1] The problem said multiple. That usually means k is not only a constant, but also an integer.
[2] That would be step-father and step-son.
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Use the ravel operator, then the sort operator, then the shape operator.
Ravel linearizes a higher-order array.
A linear array can be sorted.
The sorted linear array can then be reshaped to that of the original array.
At IBM, back in the 1960's, Ken Iverson invented APL "read A Programming
Language" that provided operators like ravel and reshape. Google it for more information.
IBM still sells a version of APL that runs on a PC.
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that's must be 4 because divide by zero.
1. there's no even prime numbers excludeing 2. so, the solution set is none {}.
2. "evenly" is the x^2/sizeof(x). however, the size of x is zero.
It's just like customers never visit the resturant, you can't tell which one of them love the food or not.
I claim it's how we describe categories of things.
No math needed...
[following added in edit]
In the case of the restaurant that has no customers,
ALL of the customers love the food. Because you can't find ONE that doesn't. and ...
NONE of the customers love the food. Because you can't find ONE that does.
It's logically ok to use universal quantifiers [all, no, none] with empty sets.
But you can't use particular quantifiers [one, some] with empty sets.
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OK, the reasoning goes like this.
According to common sense and also something called the Well-ordered Principle,
any set of numbers can be ordered, least to greatest; the only exception being
the empty set. Every non-empty set of numbers has a member which is the
smallest member of that set.
Next...
Using up to N [N is finite] syllables, in various combinations / permutations,
only a finite number of numbers can be described. For example, for N=2 those
numbers would be
1, 2, 3, 4, 5, 6, 8, 9, 10, 12 [using 1 syllable] and
7, 13, 14, 15, 16, 18, 19, 20, 30, 40, 50, 60, 80, 90 [using 2 syllables]
So those are the numbers that can be described using fewer than 3 syllables.
If it could be shown that there are no numbers that cannot be described
using fewer than 3 syllables, then these would be all the numbers that exist.
A finite number. It would be like proving there are no numbers that require
3 or more syllables.
Let's see if that's possible to do. We ask, what is the smallest number that
cannot be described using fewer than 3 syllables? Well, there is an answer
to that. It's 11 - e-lev-en - 3 syllables. There are others, of course, like 17,
21, 22, ... but 11 is the smallest one.
So there are numbers beyond those describable using fewer than 3 syllables.
But now we ask, what is the smallest number that cannot be described using
fewer than 23 syllables. Well, there seems to be an answer to that as well.
It's 1,777,777. -- 23 syllables, and no one found a smaller one.
Enter the paradox.
1,777,777 was determined to be the number that is described by the phrase
the smallest number that cannot be described using fewer than 23 syllables.
But that phrase has 22 syllables. Ooops!
By that logic 1,777,777 cannot be - nor can any other number be - the smallest
number not specifiable using fewer than 23 syllables. That is, the set of numbers
described by that phrase has no smallest member. By the well-ordered principle,
therefore, that set of numbers is empty.
Now let's talk about the set of all numbers. It comprises two subsets:
[1] the set of all numbers that can be described using fewer than 23 syllables - a finite set [since 23 is finite.]
[2] the set of all numbers that cannot be described using fewer than 23 syllables - by WOP, the empty set.
Thus the set of all numbers is finite.
What have the great brains of our time done about things like this?
They note that the heart of the paradox is that it references itself.
Rather, the answer is described on one level, and disallowed by a
description on another level. That type of paradox is called self-referential.
They deal with it by assigning its statements a level, according to a hierarchy.
Then they allow a statement to reference only those objects on its own level of hierarchy.
In this case the number of syllables in speaking the number would be on a
different hierarchical level from the number of syllables in the phrase that
describes the number. That phrase would then not be permitted to disallow
the answer found by counting syllables.
Bertrand Russel once said,
The point of philosophy is to start with something so simple as not
to seem worth stating, and to end with somethiong so paradoxical
that no one will believe it.
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Bravo cpotting and brhan. For totally different reasons.
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Barely noticed, the bell rings; and the opponents
sit quietly in their corners while their seconds
attend quickly to the cuts and bruises.
The bell rings for Round 4 ....
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Cute puzzle. I think I have the idea.
Here's a start, more to come after I get some zzzzzzzzzzz's.
----------------------------------------------------------
f1(x)={1,2,3,4} f1(x)= x cost = 0
f2(x)={1,2,4,3} f2(x)=?
f3(x)={1,3,2,4} f3(x)=?
f4(x)={1,3,4,2} f4(x)=?
f5(x)={1,4,2,3} f5(x)=?
f6(x)={1,4,3,2} f6(x)=? 4-(x+2)%4 cost=3
----------------------------------------------------------
f7(x)={2,1,3,4} f7(x)=?
f8(x)={2,1,4,3} f8(x)=? 4-(x+1)%4 cost=3
f9(x)={2,3,1,4} f9(x)=?
f10(x)={2,3,4,1} f10(x)=? 1+x%4 cost=2
f11(x)={2,4,1,3} f11(x)=?
f12(x)={2,4,3,1} f12(x)=?
----------------------------------------------------------
f13(x)={3,1,2,4} f13(x)=?
f14(x)={3,1,4,2} f14(x)=?
f15(x)={3,2,1,4} f15(x)=? 4-x%4 cost=2
f16(x)={3,2,4,1} f16(x)=?
f17(x)={3,4,1,2} f17(x)=? 1+(x+2)%4 cost=3
f18(x)={3,4,2,1} f18(x)=?
----------------------------------------------------------
f19(x)={4,1,2,3} f19(x)=? 1+(x+2)%4 cost=3
f20(x)={4,1,3,2} f20(x)=?
f21(x)={4,2,1,3} f21(x)=?
f22(x)={4,2,3,1} f22(x)=?
f23(x)={4,3,1,2} f23(x)=?
f24(x)={4,3,2,1} f24(x)= 5-x cost = 1
----------------------------------------------------------
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I did this, once, back in school.
It was a computer game, and there were colors instead of numbers,
and there could be repeats.
I'll try to work this out later,
but right now my intuition is saying it can be done in ...
8 tries.
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Seven to go, and my brain is mush tonight ...
14 15 P in a R T
15 3 W on a T
17 11 P in a F (S) T
24 13 L in a B D
26 9 L of a C
30 9 P in S A
31 6 B to an O in C
I wondered whether 17 is 11 Players in [on?] a Football Team ... but what is the S?
Not knowing anything about soccer, does that apply?
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If your choice is [3], it's correct; but ...All even numbers [excluding 2] are evenly divisable by 2, and therefor not prime. Therefor there are NO EVEN PRIME NUMBERS if 2 is excluded. Hence no even prime numbers which would be evenly divisable by 5!There you have it!
Why is it the best answer?
Why did you pick it over [1] All even prime numbers [excluding 2] are divisible by 5?
Aren't they all divisible by 5? Show me one that is not.
[red text edited]
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Oh ... we never got to the paradox. Let's try again:
Bravo, Writersblock.1,177,777
one million, one hundred seventy seven thousand, seven hundred seventy seven = 23 syllables
One-mill-ion sev-en hund-red sev-en-ty sev-en thou-sand sev-en hund-red sev-en-ty sev-en = 23.
1,777,777 is the smallest number not specifiable using fewer than twenty-three syllables.
At least, no one has come up with a smaller number. So let's say it is.
You get the prize.
O wait. This is supposed to be a paradox.
ummm, just for the heck of it, count the syllables in red, above.
If the red words specified your answer, then ....
ummm, just for the heck of it, count the syllables in red, above.
the smal-lest num-ber not spe-ci-fi-a-ble us-ing few-er than twen-ty-three syl-la-bles.
If the red words specified the answer, then ....
The smallest number not specifiable using fewer than twenty-three syllables has just been specified using fewer than twenty-three syllables.
Which leads to the conclusion that there is only a finite number of natural numbers.
Good old Berry ...
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7. 13 stripes in the U.S. flag
12. 3 blind mice?
19. 13 is unlucky for some
28. 23 Pairs of chromosomes in the human body
29. 64 squares on a chess (checkers) board
33. 15 men on a dead man's chest
hah! yes ... See How They Run! cute.
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My picks:
[1] and [3] --- originally I picked only [1] but I changed my mind, making the problem a little less satisfying. <!-- s:oops: --><!-- s:oops: -->
[4] is out ... some answers have been defended, and
[2] is out ... because of existential import.
Let's examine [1]-[3] by restating them as categorical propositions.
Big words ... they just mean statements that relate members of categories of things.
The categories in the statements are their Subjects and their Predicates [P].
Let S = numbers that are even primes, excluding 2
Let P = numbers that are [evenly] divisible by 5.
Then the options become
[1] All S is P
[2] Some S is P
[3] No S is P
It's been noted that S has no members. S is an empty set.
That means we have to eliminate [2]. Why?
In Boolean logic, the categorical proposition Some S is P carries the assertion that S has at least one member.
That is, in Boolean logic, the word Some means at least one.
Logicians call this "existential import" [EI].
But [1] and [3] are OK.
"All" and "None" do not assert the existence of even one member of the category. They don't have EI.
It makes logical sense to say
[1] All five-headed women have two toes.
[3] No five-headed women have two toes.
Why do these statement make sense? Because their logically contradictory statements are false.
[1a] Some five-headed women do not have two toes. This is false because of EI.
[3a] Some five-headed women do have two toes. This is also false because of EI.
Originally, I thought I could exclude [3] by saying "None" meant "Not one"
and then asserting that "Not one" implied there was at least one, simply
because we talked about it.
Nah ... upon reflection, can't do that.
So my picks are ... [1] and [3] - equally sensible.
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Hmmm....
Ok; so there is a finite number of numbers.
No biggie, I guess.
After all, there is also only a finite number of textbooks to be re-written.
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I can add ...
3 7 Wonders of the World
5 66 Books of the Bible
9 39 Books of the Old Testament
10 5 Toes on a Foot [?]
11 90 Degrees in a Right Angle
13 32 is the Temperature in Degrees Farenheit at which Water Freezes
16 100 Cents in a Dollar
18 12 Months in a Year
21 29 Days in February in a Leap Year
22 27 Books in the New Testament
32 1000 Years in a Millenium
That leaves ....
7 13 S in the U S F
12 3 B M (S H T R)
14 15 P in a R T
15 3 W on a T
17 11 P in a F (S) T
19 13 is U F S
24 13 L in a B D
26 9 L of a C
28 23 P of C in the H B
29 64 S on a C B
30 9 P in S A
31 6 B to an O in C
33 15 M on a D M C
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I thought it looked like Monterey CA's Lone Cypress tree.
[url:f3fc2]http://www.beachcalifornia.com/lone-cypress-tree.html
Maybe not. One Tree Hill fits also.
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It's not something from the original Zork, cave, is it? XYZZY!!?
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Sure. I'm still clueless and feeling badly because of it.
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Found this while rummaging around for new stuff.
Haven't seen it before, and don't have a clue.
1 - Fresh fish and lamb from Korea
2 - Korean literature from the same church leader
3 - A wild bonfire
4 - Freddy the Queen
5 - The other missile in the cuban crisis
6 - It started with a riff, the one from Pinball Wizard
7 - Large addition to Stewart Copeland's drumkit
What are these seven things and why? what do they represent in the order persented?
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1 26 L of the A
2 7 D of the W
3 7 W of the W
4 12 S of the Z
5 66 B of the B
6 52 C in a P (W J)
7 13 S in the U S F
8 18 H on a G C
9 39 B of the O T
10 5 T on a F
11 90 D in a R A
12 3 B M (S H T R)
13 32 is the T in D F at which W F
14 15 P in a R T
15 3 W on a T
16 100 C in a D
17 11 P in a F (S) T
18 12 M in a Y
19 13 is U F S
20 8 T on an O
21 29 D in F in a L Y
22 27 B in the N T
23 365 D in a Y
24 13 L in a B D
25 52 W in a Y
26 9 L of a C
27 60 M in an H
28 23 P of C in the H B
29 64 S on a C B
30 9 P in S A
31 6 B to an O in C
32 1000 Y in a M
33 15 M on a D M C
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Oops, 66 repeats 21.
I'll contribute one to keep the count right,
71. The Cranberries [lower right]
[url:a670f]http://www.cranberries.com/
Find Nth in P(M,K) or C(M,K).
in New Logic/Math Puzzles
Posted
How do you determine an order? Without that, what does Nth mean?