Einstein's Riddle

[quote]Professor X wrote:
It’s the only reason I play Tomb Raider even now.[/quote]

Uh…huh.

[quote]ukrainian wrote:
I got the OP’s riddle.

Riddle 1:

His Birthday’s on December 31st, and it is January 1st.

Riddle 2:

He’s going at 45 km/h.

Sign one is kilometer 16.

Sign two is kilometer 61.

Sign three is kilometer 106.[/quote]

Mind me asking how found that out?
I set it up as an arithmetic sequene so:
XY= U1
YX= U2
X0Y=U3
therefore
XY+d=YX

YX+d=X0Y
YX=X0Y-D
by setting them equal
XY+d= X0Y-d
XY+2d=X0Y
from here I have no idea where to go though. Did you do something along these lines, or something completely different?

[quote]FormerlyTexasGuy wrote:
300andabove wrote:
Play…

Can you find the C ? ( Good exercise for the eyes! )

OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOCOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO

Once you?ve found the C?

Find the 2 letters B!

RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRBRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRBRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR

Once you?ve found the letters B

Find the 1

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII1III
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Once you?ve found the 1…

Find the 6

9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999699999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999

Once you?ve found the 6…

Find the N ( More difficult ! )

MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMNMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM

Once you?ve found the N…

Find the Q…

OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOQOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO

Interesting. I found all of them before I even looked - while I was reading the instructions. [/quote]

[quote]PonceDeLeon wrote:
Professor X wrote:
It’s the only reason I play Tomb Raider even now.

Uh…huh.

[/quote]

What?

[quote]Professor X wrote:
PonceDeLeon wrote:
Professor X wrote:
It’s the only reason I play Tomb Raider even now.

Uh…huh.

What?[/quote]

Usually it’s for the right reason. And the left reason. Nice pair of reasons.

[quote]pookie wrote:
Professor X wrote:
PonceDeLeon wrote:
Professor X wrote:
It’s the only reason I play Tomb Raider even now.

Uh…huh.

What?

Usually it’s for the right reason. And the left reason. Nice pair of reasons.
[/quote]

Oh.

Well.

Those are great too. Being able to pick daisy duke shorts for her to run through the jungle with helps also.

[quote]300andabove wrote:
Play…

Can you find the C ? ( Good exercise for the eyes! )

OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOCOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOO

Once you?ve found the C?

Find the 2 letters B!

RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRBRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRBRRRRRRRRRRRRRRRRRRRRR
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR

Once you?ve found the letters B

Find the 1

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII1III
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Once you?ve found the 1…

Find the 6

9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999699999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999
9999999999999999999999999999999999

Once you?ve found the 6…

Find the N ( More difficult ! )

MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMNMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM
MMMMMMMMMMMMM

Once you?ve found the N…

Find the Q…

OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOQOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOO

[/quote]

I got all of these immediately, but had trouble with the riddles.

[quote]Scorzerci wrote:
ukrainian wrote:
I got the OP’s riddle.

Riddle 1:

His Birthday’s on December 31st, and it is January 1st.

Riddle 2:

He’s going at 45 km/h.

Sign one is kilometer 16.

Sign two is kilometer 61.

Sign three is kilometer 106.

Mind me asking how found that out?
I set it up as an arithmetic sequene so:
XY= U1
YX= U2
X0Y=U3
therefore
XY+d=YX

YX+d=X0Y
YX=X0Y-D
by setting them equal
XY+d= X0Y-d
XY+2d=X0Y
from here I have no idea where to go though. Did you do something along these lines, or something completely different?

[/quote]

Between sign 1 & 2 you know his speed is a 2-digit number. Since at sign 2 he has traveled only a 2 digit number of miles and the same amount of time has passed between sign 2 and 3, you know that X0Y is less that 200, and X=1. A little trial and error should lead you to Y=6 fairly quick.

If you really wanted to set up a formula I would let
a=first sign distance
b=second sign distance
c=third sign distance.

Then
a=10x + y
b=10y + x
c=100x + y
and
c-b=b-a

Substituting for the last equation you have:
100x + y - 10y - x = 10y + x - 10x -y
99x - 9y = 9y -9x
11x - y = y - x
12x=2y
6x=y

So
a=16x
b=61x
c=106x

From the problem we know that a and b are integers and <100. Since 61 is prime the only value for x that could satisfy those two conditions is 1.

[quote]Scorzerci wrote:
ukrainian wrote:
I got the OP’s riddle.

Riddle 1:

His Birthday’s on December 31st, and it is January 1st.

Riddle 2:

He’s going at 45 km/h.

Sign one is kilometer 16.

Sign two is kilometer 61.

Sign three is kilometer 106.

Mind me asking how found that out?
I set it up as an arithmetic sequene so:
XY= U1
YX= U2
X0Y=U3
therefore
XY+d=YX

YX+d=X0Y
YX=X0Y-D
by setting them equal
XY+d= X0Y-d
XY+2d=X0Y
from here I have no idea where to go though. Did you do something along these lines, or something completely different?

[/quote]

I did try to set up some kind of sequence as well, but it didn’t work. I knew the X=1 because the his rate would not get him to X0Y in the same time it did to YX if X>1. After that I just did some guess and check. I tried 5 first but that didn’t work, then I tried 6 and it did.

I know equations and sequences are fun, but most puzzles make it so you can’t use it.

[quote]tedro wrote:
Scorzerci wrote:
ukrainian wrote:
I got the OP’s riddle.

Riddle 1:

His Birthday’s on December 31st, and it is January 1st.

Riddle 2:

He’s going at 45 km/h.

Sign one is kilometer 16.

Sign two is kilometer 61.

Sign three is kilometer 106.

Mind me asking how found that out?
I set it up as an arithmetic sequene so:
XY= U1
YX= U2
X0Y=U3
therefore
XY+d=YX

YX+d=X0Y
YX=X0Y-D
by setting them equal
XY+d= X0Y-d
XY+2d=X0Y
from here I have no idea where to go though. Did you do something along these lines, or something completely different?

Between sign 1 & 2 you know his speed is a 2-digit number. Since at sign 2 he has traveled only a 2 digit number of miles and the same amount of time has passed between sign 2 and 3, you know that X0Y is less that 200, and X=1. A little trial and error should lead you to Y=6 fairly quick.

If you really wanted to set up a formula I would let
a=first sign distance
b=second sign distance
c=third sign distance.

Then
a=10x + y
b=10y + x
c=100x + y
and
c-b=b-a

Substituting for the last equation you have:
100x + y - 10y - x = 10y + x - 10x -y
99x - 9y = 9y -9x
11x - y = y - x
12x=2y
6x=y

So
a=16x
b=61x
c=106x

From the problem we know that a and b are integers and <100. Since 61 is prime the only value for x that could satisfy those two conditions is 1.[/quote]

Wow, I can’t believe I didn’t think of this. I am dumb.

[quote]tedro wrote:
If you really wanted to set up a formula I would let
a=first sign distance
b=second sign distance
c=third sign distance.

Then
a=10x + y
b=10y + x
c=100x + y
and
c-b=b-a

Substituting for the last equation you have:
100x + y - 10y - x = 10y + x - 10x -y
99x - 9y = 9y -9x
11x - y = y - x
12x=2y
6x=y

So
a=16x
b=61x
c=106x

From the problem we know that a and b are integers and <100. Since 61 is prime the only value for x that could satisfy those two conditions is 1.[/quote]
Good thinking… Thanks!

[quote]ukrainian wrote:
Wow, I can’t believe I didn’t think of this. I am dumb.[/quote]
Yeah once you’ve seen it, it seems pretty obvious. I have to say, I really find applied maths like this fun.
(yes I’m a bit of a dork)

[quote]ukrainian wrote:
tedro wrote:
Scorzerci wrote:
ukrainian wrote:
I got the OP’s riddle.

Riddle 1:

His Birthday’s on December 31st, and it is January 1st.

Riddle 2:

He’s going at 45 km/h.

Sign one is kilometer 16.

Sign two is kilometer 61.

Sign three is kilometer 106.

Mind me asking how found that out?
I set it up as an arithmetic sequene so:
XY= U1
YX= U2
X0Y=U3
therefore
XY+d=YX

YX+d=X0Y
YX=X0Y-D
by setting them equal
XY+d= X0Y-d
XY+2d=X0Y
from here I have no idea where to go though. Did you do something along these lines, or something completely different?

Between sign 1 & 2 you know his speed is a 2-digit number. Since at sign 2 he has traveled only a 2 digit number of miles and the same amount of time has passed between sign 2 and 3, you know that X0Y is less that 200, and X=1. A little trial and error should lead you to Y=6 fairly quick.

If you really wanted to set up a formula I would let
a=first sign distance
b=second sign distance
c=third sign distance.

Then
a=10x + y
b=10y + x
c=100x + y
and
c-b=b-a

Substituting for the last equation you have:
100x + y - 10y - x = 10y + x - 10x -y
99x - 9y = 9y -9x
11x - y = y - x
12x=2y
6x=y

So
a=16x
b=61x
c=106x

From the problem we know that a and b are integers and <100. Since 61 is prime the only value for x that could satisfy those two conditions is 1.

Wow, I can’t believe I didn’t think of this. I am dumb.[/quote]

Come on guys. Guess and check was the quickest.

Y>X and X is non-zero. make a guess based on YX being halfway between XY a X0Y. If it is more than half lower Y or raise X. It was pretty apparent X was one. as 20Y+ was too big. It took me 2 guess and about 20 seconds.

[quote]Scorzerci wrote:
tedro wrote:
If you really wanted to set up a formula I would let
a=first sign distance
b=second sign distance
c=third sign distance.

Then
a=10x + y
b=10y + x
c=100x + y
and
c-b=b-a

Substituting for the last equation you have:
100x + y - 10y - x = 10y + x - 10x -y
99x - 9y = 9y -9x
11x - y = y - x
12x=2y
6x=y

So
a=16x
b=61x
c=106x

From the problem we know that a and b are integers and <100. Since 61 is prime the only value for x that could satisfy those two conditions is 1.
Good thinking… Thanks!

ukrainian wrote:
Wow, I can’t believe I didn’t think of this. I am dumb.
Yeah once you’ve seen it, it seems pretty obvious. I have to say, I really find applied maths like this fun.
(yes I’m a bit of a dork)

[/quote]

It’s alright. I find them fun too.

[quote]ukrainian wrote:
Scorzerci wrote:
tedro wrote:
If you really wanted to set up a formula I would let
a=first sign distance
b=second sign distance
c=third sign distance.

Then
a=10x + y
b=10y + x
c=100x + y
and
c-b=b-a

Substituting for the last equation you have:
100x + y - 10y - x = 10y + x - 10x -y
99x - 9y = 9y -9x
11x - y = y - x
12x=2y
6x=y

So
a=16x
b=61x
c=106x

From the problem we know that a and b are integers and <100. Since 61 is prime the only value for x that could satisfy those two conditions is 1.
Good thinking… Thanks!

ukrainian wrote:
Wow, I can’t believe I didn’t think of this. I am dumb.
Yeah once you’ve seen it, it seems pretty obvious. I have to say, I really find applied maths like this fun.
(yes I’m a bit of a dork)

It’s alright. I find them fun too.[/quote]

WOOOHOOOO! Any other math team nerds?

[quote]DoubleDuce wrote:
WOOOHOOOO! Any other math team nerds?[/quote]

There wasn’t a math team at any of the school’s I went to. There was math club in college, but that was a bit too nerdy. No fun puzzles, 1 competition per year, and a bunch of geeks.

I always wanted to be on a math team though.

[quote]tedro wrote:
DoubleDuce wrote:
WOOOHOOOO! Any other math team nerds?

There wasn’t a math team at any of the school’s I went to. There was math club in college, but that was a bit too nerdy. No fun puzzles, 1 competition per year, and a bunch of geeks.

I always wanted to be on a math team though.[/quote]

I was on it through middle school and high school. It was a lot of fun. Got to go on some trips every year to some cool places. Most of the stuff is word problems like mentioned above.

[quote]DoubleDuce wrote:
tedro wrote:
DoubleDuce wrote:
WOOOHOOOO! Any other math team nerds?

There wasn’t a math team at any of the school’s I went to. There was math club in college, but that was a bit too nerdy. No fun puzzles, 1 competition per year, and a bunch of geeks.

I always wanted to be on a math team though.

I was on it through middle school and high school. It was a lot of fun. Got to go on some trips every year to some cool places. Most of the stuff is word problems like mentioned above.[/quote]

I never really was on the math team, but I am in AP Calc BC right now, so I guess that’s still good enough.

Still, I have always liked solving equations. Don’t know why, but I did. There are some that we have now in our class that just make me go, “What the fuck are they asking me?”

For those who like math/computer problems: http://projecteuler.net/