Bat and Ball

[Martin]

BLACK

CLACK

CLICK

CRICK (not in original answer)

TRICK

TRICE

TRITE

WRITE

WHITE

 

Thats a tough one. I'll bet there's a shorter way.

 

this is Deified answer with a correction suggested by Jdurg

so if we were keeping score the two of them would split a point.

 

For anybody new, the challenge was to get from black to white CHANGING ONLY ONE LETTER AT A TIME and have it be ordinary English words at each step. Nobody in this thread has offered any shorter series of moves.

[Deified]

Deified, I dont see how to do this one. Want to give a hint?

 

Think "acceleration".

 

The first zero is not really part of the pattern, it's just the null state.

[Martin]

Here is a number puzzle I created the other day. I think it's pretty hard.

 

Find the next number:

 

0' date=' 1, 1, 0, -1, 0, 6...[/quote']

 

.....

Think "acceleration".

 

The first zero is not really part of the pattern, it's just the null state.

 

Deified, I still dont get it. wish someone else would try.

[Deified]

Another hint: five variables needed. Think about it as though it were an object with forces working on it. (note the plural) The last trick, I leave to you.

[Kingpin1989]

I'm gonna have to say the next number is six, and I reason it this way...the difference in the two numbers is the next number, only excepting that -1 to 0 is no a change of zero. So I'm probly wrong, but that's my guess.

[Martin]

Originally Posted by Deified

 

Here is a number puzzle I created the other day. I think it's pretty hard.

 

Find the next number:

 

0, 1, 1, 0, -1, 0, 6...

 

Let's imagine that the next number is 21 and the one after that is 50

now we look at the new sequence

 

0, 1, 1, 0, -1, 0, 6, 21 , 50 , ...

 

Does this have any recognizable pattern?

 

well the sequence of differences is:

 

1, 0, -1, -1, 1, 6, 15, 29 , ...

 

and the next sequence of differences is:

 

-1, -1, 0, 2, 5, 9, 14 ,...

 

and the next sequence of differences is:

 

0, 1, 2, 3, 4, 5...

 

dont know whether you'd call that a pattern or not

 

is Defied still around? this problem Defies me.

[Deified]

Yes I am still around. And no, you haven't found the solution. If you like, I will give the answer.

[Martin]

Yes I am still around. And no, you haven't found the solution. If you like, I will give the answer.

 

definitely! I would like that very much. Please give the answer immediately!

[Deified]

When I created this problem I had been reading the SciAm article on the big bang and the expansion of space. They said something about acceleration of expansion and then what would happen if the acceleration were accelerating or something along those lines. It was a while ago. So I began to think. "what if you had layers of acceleration? all accelerating each other? Maybe some deceleration too? What would the result be? The result was a pretty tricky math puzzle. Here is what i did:

 

x=objects acceleration

y=x's acceleration

z=y's acceleration

c= any constant. In this case 1

d=objects deceleration

p=resultant motion

 

So we start with x=0, y=0, z=0, c=1, d=1(!the trick!), p=0

I will write it as if it were a generic programming language.

 

p=p+x

p=p+d

x=x+y

y=y+z

z=z+c

d=d-c

 

so we get the pattern

 

0 0 0 0 1

1 0 0 1 0

1 0 1 2 -1

0 1 3 3 -2

-1 4 6 4 -3

0 10 10 5 -4

6 20 15 6 -5

21 35 21 7 -6

50 51 28 8 -7

 

21 is the number I was looking for, amazingly you came up with it using some other process. Its pretty impressive that you got the next two digits correctly. I still don't understand what exactly you did. Care to explain again?

[Deified]

I suppose our methods correlate in some way that is well beyond my grasp at this late hour.

[Martin]

21 is the number I was looking for, amazingly you came up with it using some other process. Its pretty impressive that you got the next two digits correctly...

 

 

I think newton (and probably his contemporaries) used this kind of techique

it is called "first difference", "second difference", etc.

 

I am very glad that my answer is correct and that the problem is solved!

 

that was a nice problem

 

would you like to post another one (can be word prblm, logic, arithm, you name it!)

[Apple3.14]

If you accept formal names, then I have one step better for you...

 

BLACK

BLICK - http://dictionary.reference.com/search?q=blick

BRICK

BRICE - Normal First Name

TRICE

TRITE

WRITE

WHITE

[Callipygous]

except, or accept? im not sure which you mean in this case and they have just about opposite meanings in this context.

[Apple3.14]

woops ... my mistake. (see what happens when you don't get enough sleep? You can make the dumbest mistakes)

 

corrected to read: "if you accept"

[Martin]

If you accept formal names' date=' then I have one step better for you...

 

BLACK

BLICK - http://dictionary.reference.com/search?q=blick

BRICK

BRICE - Normal First Name

TRICE

TRITE

WRITE

WHITE[/quote']

 

Apple, I am so glad someone is trying to turn black to white. Actually I did not count on anyone using proper names but only words. BTW I used your dictionary link to look up "brack" and it gave two meanings!

 

http://dictionary.reference.com/search?q=brack

 

(both refer back to Webster's dictionary which is pretty standard so I guess it must be a word)

 

Care to try again? Get rid of the name Brice and do it all with just words?

[The Thing]

BLACK

SLACK

SLICK

SLICE

SPICE

SPITE

SHITE (OMG I can't believe I used this word. It is a real word but it is quite disgusting. But it is a real word. http://dictionary.reference.com/search?q=Shite

WHITE

[Martin]

BLACK

SLACK

SLICK

SLICE

SPICE

SPITE

SHITE (OMG I can't believe I used this word. It is a real word but it is quite disgusting. But it is a real word. http://dictionary.reference.com/search?q=Shite

WHITE

 

that is very good.

 

I do not know any shorter path.

 

the theoretical minimum would be 5 moves, and you did it in 7 moves (so the list of words is 8 long)

 

I personally have never seen anyone do it in fewer moves. but maybe we should wait a day or so and see if anyone (including you) can better it

[Apple3.14]

BLACK

SLACK

SLICK

SLICE

SLITE -- Webster's is saying it is one of their words, but is not letting me log into to actually confirm its definition. - can you confirm it?

SHITE

WHITE

[Newtonian]

that is very good.

 

I do not know any shorter path.

 

the theoretical minimum would be 5 moves' date=' and you did it in 7 moves (so the list of words is 8 long)

 

I personally have never seen anyone do it in fewer moves. but maybe we should wait a day or so and see if anyone (including you) can better it[/quote']

Martin you may have missed post 24 then....I think one of our respected members has already blown everyone away with the minimum moves possible.

[Algebracus]

The rules were obviously not written clearly enough: I suppose that when you go from a word to another, the rule was supposed to be that only one letter can be changed, counting a rearrangement of the letters as a change of at least two letters. If a rearrangement is not counted as a change, then Newtonian surely is better off.

 

Doing it in only five steps, not allowing rearrangements, is impossible, given the rule that every accepted word has to be encountered at http://dictionary.reference.com (I find such a rule much better than a rule talking about "real words". What does that mean?):

 

Black - bhack, wlack, blick, blatk or blace

Of these, only blick is allowed.

Blick - wlick, bhick, blitk or blice

Of these, not a single one is allowed.

[Martin]

The rules were obviously not written clearly enough: I suppose that when you go from a word to another' date=' the rule was supposed to be that only one letter can be changed, counting a rearrangement of the letters as a change of at least two letters. If a rearrangement is not counted as a change, then Newtonian surely is better off.

 

Doing it in only five steps, not allowing rearrangements, is impossible, given the rule that every accepted word has to be encountered at http://dictionary.reference.com (I find such a rule much better than a rule talking about "real words". What does [i']that[/i] mean?):

 

Black - bhack, wlack, blick, blatk or blace

Of these, only blick is allowed.

Blick - wlick, bhick, blitk or blice

Of these, not a single one is allowed.

 

bravo! you have proved it like a true mathematician would

 

it is not possible to do in 5 moves! (the "Agebracus theorem")

 

I consider that permutation changes several letters

what I mean by "change one letter" means only just that: do not disturb the others by changing the order

[Martin]

BLACK

SLACK

SLICK

SLICE

SLITE -- Webster's is saying it is one of their words' date=' but is not letting me log into to actually confirm its definition. - can you confirm it?

SHITE

WHITE[/quote']

 

we seem to have evolved a clarification of the rules.

Algebracus just announced it: use

http://dictionary.reference.com/

to see if it is a valid word

 

I checked to see if "slite" is acceptable by that criterion and regret that I must inform you that it is not

http://dictionary.reference.com/search?q=slite

 

good try however!

likewise kudos to newtonian who, however, was working on a different puzzle since he differed in his understanding of the rules.

 

I declare that the winner is THE THING

[Apple3.14]

Yeah, I noticed dictionary.com didn't have it too.

 

I get "One entry found for Slite." when I got to webster's site though.

 

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=slite

 

I just want to knwo what they are finding, because I cant seem to log in and check.

 

Alas, I accept defeat. My hat's off to The Thing.

[Martin]

?, 11, 20, 31, 44, 61, 100, ???

 

can anyone guess the two terms at the ends:

the one (?) before and the one (???) after

[Ducky Havok]

I was going to answer this, but then I realized it was just like the other one I got in the word puzzle thread so I figure I'll let someone else get it.