Logs are stacked in a Cold Deck. Looking at the stack from the butt end, they form a pyramid shape. The end of each log is painted either Red, Yellow, or Blue. Logs painted the same color cannot touch each other. The sketch below shows Two logs already painted. What color will log X be painted?
chrissy you say blue, jimbo1 you say it's red and i'll go with yellow.
mmmmmmmmmmm
tomk it's yellow
don't have the time to work it out logically now but will later..
probably going to take me all week too.
unless i've made a mistake, looks like you'd have been right jimbo1,
tomk it's red,
first i numbered all the logs 1 to 28 starting from the top and always starting next number from the left on lower row,
then wrote down all the numbers with the 3 colours next to them
then wrote down all the ones it connects to meaning they can't be the same colour so as soon as i find out a colour i could cross that colour off from all the ones it connects too.
then using both lists started a process of elimination crossing off the colours as i went along.
log number 1 (highest) can't be blue because it touches the known blue log(number 2)
it can't be yellow because it left me with only red or blue for logs 8 and 9 both touching each other so can't be same colour and also touching log 13(known red) so can't be red, therefore a dead end, meaning log 1 must be red.
so starting with red for log 1, i started again and ended up with log 28 (the X) as having a choice of r/y but log 27 was y so stopped there because 28 could only be r
hope that makes at least a little bit of sense..
anyway answer is RED
noooooooooooooooooooooooooo took me that long to make my post Nahumi got in there first..
well done Nahumi, i agree.
Congratulations Nahumi for being the first to provide the correct answer.
The log with the X will indeed be Red.
Another way to look at the solution, besides actually coloring them all in, is to consider that because no like colored logs can touch…. there is a "protective" circle around each log that makes a pattern of what can't match colors as well as what must match color. If we started at log X and "greyed out" the logs that cannot be it's color… we would get a diagram like this: [external image: Posted Image]
As b]Nahumi has already shown… the already painted red log falls into the "must match" category.
(It's to hard for me to fill in all of the colors of all of the logs in my head so I had to come up with another way to solve it…. and I can do the "must match" pattern in my head)
Sometimes the simplest solution is the most elegant.
All I knew is that each log around the red one couldn't be red, which meant that the one immediatly lower left and lower right of the blue had to be yellow and red respectively.
From there you just repeat the pattern out. You take any two adjecent logs and whichever colour is missing is the colour of the log that is in common with both and completes a three point triangle.
What you notice then is that each colour holds the same tesselating pattern (it has to tesselate and the pattern has to be symmetrical because the triangle is equillateral. It would be a different story if the triangle was anything else) and that you just offset the pattern for each colour.
But that takes longer to figure out… so you might as well go for the simple option.
unless i've made a mistake, looks like you'd have been right jimbo1,
tomk it's red,
first i numbered all the logs 1 to 28 starting from the top and always starting next number from the left on lower row,
then wrote down all the numbers with the 3 colours next to them
then wrote down all the ones it connects to meaning they can't be the same colour so as soon as i find out a colour i could cross that colour off from all the ones it connects too.
then using both lists started a process of elimination crossing off the colours as i went along.
log number 1 (highest) can't be blue because it touches the known blue log(number 2)
it can't be yellow because it left me with only red or blue for logs 8 and 9 both touching each other so can't be same colour and also touching log 13(known red) so can't be red, therefore a dead end, meaning log 1 must be red.
so starting with red for log 1, i started again and ended up with log 28 (the X) as having a choice of r/y but log 27 was y so stopped there because 28 could only be r
hope that makes at least a little bit of sense..
anyway answer is RED
noooooooooooooooooooooooooo took me that long to make my post Nahumi got in there first..
That was pretty easy… so…. here is another easy one… though the hard part may be for some of you to provide an answer.
An old man passed away leaving 4 heirs. He had a piece of property that he left to all 4 of them to be divided amongst them with the stipulation that each of the siblings property would have the same shape. If the property had been a perfect square… this would have been simple… but it wasn't. They found that the Posts on the fence delineating the extremities of the parcel were spaced evenly so they used this pattern to place more posts across the field - forming a grid - to help with the task of division. [external image: Posted Image]
Using these posts, where should the divider fence(s) be located?
mmmmmmmmmmm
tomk it's yellow
don't have the time to work it out logically now but will later..
probably going to take me all week too. 
All I knew is that each log around the red one couldn't be red, which meant that the one immediatly lower left and lower right of the blue had to be yellow and red respectively.
From there you just repeat the pattern out. You take any two adjecent logs and whichever colour is missing is the colour of the log that is in common with both and completes a three point triangle.
What you notice then is that each colour holds the same tesselating pattern (it has to tesselate and the pattern has to be symmetrical because the triangle is equillateral. It would be a different story if the triangle was anything else) and that you just offset the pattern for each colour.
But that takes longer to figure out… so you might as well go for the simple option. 
