Christmas conundrum

[earendel]

One of my fellow employees brought this to me - evidently it was a question at a Christmas party at her church. Although my math skills are fair, I can't seem to get a handle on the answer, so I figured I'd post it here.

In an open field there are 5 Christmas trees decorated with colors. The red Christmas tree and the orange Christmas tree are 10 yards apart. The yellow Christmas tree is 12 yards from the red Christmas tree. The blue Christmas tree is 14 yards from the oak tree. The pink Christmas tree is 17 yards from the blue Christmas tree. The yellow Christmas tree and the Orange Christmas tree are 9 yards apart. The yellow Christmas tree and the pink Christmas tree are 13 yards apart. The pink Christmas tree and the orange Christmas tree are 11 yards apart. How far is the blue Christmas tree from the red Christmas tree (rounded to the nearest yard)?

[MarleysGh0st]

One of my fellow employees brought this to me - evidently it was a question at a Christmas party at her church. Although my math skills are fair, I can't seem to get a handle on the answer, so I figured I'd post it here.

In an open field there are 5 Christmas trees decorated with colors. The red Christmas tree and the orange Christmas tree are 10 yards apart. The yellow Christmas tree is 12 yards from the red Christmas tree. The blue Christmas tree is 14 yards from the oak tree. The pink Christmas tree is 17 yards from the blue Christmas tree. The yellow Christmas tree and the Orange Christmas tree are 9 yards apart. The yellow Christmas tree and the pink Christmas tree are 13 yards apart. The pink Christmas tree and the orange Christmas tree are 11 yards apart. How far is the blue Christmas tree from the red Christmas tree (rounded to the nearest yard)?

Unless there was some more information about the configuration of the trees, I'd say there's not enough information to solve this. Are they planted all in one line? In a square grid? The blue tree is only measured in relation to the pink one and to the oak, which isn't measured in relation to any other, so the blue tree could be anywhere in a 17 yard circle around the pink one.

[fantine33]

One of my fellow employees brought this to me - evidently it was a question at a Christmas party at her church. Although my math skills are fair, I can't seem to get a handle on the answer, so I figured I'd post it here.

In an open field there are 5 Christmas trees decorated with colors. The red Christmas tree and the orange Christmas tree are 10 yards apart. The yellow Christmas tree is 12 yards from the red Christmas tree. The blue Christmas tree is 14 yards from the oak tree. The pink Christmas tree is 17 yards from the blue Christmas tree. The yellow Christmas tree and the Orange Christmas tree are 9 yards apart. The yellow Christmas tree and the pink Christmas tree are 13 yards apart. The pink Christmas tree and the orange Christmas tree are 11 yards apart. How far is the blue Christmas tree from the red Christmas tree (rounded to the nearest yard)?

The Blue tree is only mentioned in conjunction with the oak tree, and vice versa. Assuming that an oak tree is not a Christmas tree, I would think that you have no way to tell.

I'm only gauging this off of doing logic puzzles, because math makes my head explode.

[fantine33]

One of my fellow employees brought this to me - evidently it was a question at a Christmas party at her church. Although my math skills are fair, I can't seem to get a handle on the answer, so I figured I'd post it here.

In an open field there are 5 Christmas trees decorated with colors. The red Christmas tree and the orange Christmas tree are 10 yards apart. The yellow Christmas tree is 12 yards from the red Christmas tree. The blue Christmas tree is 14 yards from the oak tree. The pink Christmas tree is 17 yards from the blue Christmas tree. The yellow Christmas tree and the Orange Christmas tree are 9 yards apart. The yellow Christmas tree and the pink Christmas tree are 13 yards apart. The pink Christmas tree and the orange Christmas tree are 11 yards apart. How far is the blue Christmas tree from the red Christmas tree (rounded to the nearest yard)?

Unless there was some more information about the configuration of the trees, I'd say there's not enough information to solve this. Are they planted all in one line? In a square grid? The blue tree is only measured in relation to the pink one and to the oak, which isn't measured in relation to any other, so the blue tree could be anywhere in a 17 yard circle around the pink one.

Oh, I totally missed the line about the pink and blue trees (I have reading issues). I think in that case there would be some way to figure it out, since each tree is mentioned in relation to two others. But I'm obviously not the arithmegician to figure it out.

And Ah Helped! ha!

[MarleysGh0st]

Oh, I totally missed the line about the pink and blue trees (I have reading issues). I think in that case there would be some way to figure it out, since each tree is mentioned in relation to two others. But I'm obviously not the arithmegician to figure it out.

And Ah Helped! ha!

If the oak tree was measured in relation to a second tree, we could figure this out with some trigonometry, but it's only related to the blue one. That means the oak is free to swing around the blue tree, and so the blue tree is free to swing around the pink one. So to speak...

Was this puzzle given to you on paper or orally, ear? I'm betting that something's been left out.

[fantine33]

Oh, I totally missed the line about the pink and blue trees (I have reading issues). I think in that case there would be some way to figure it out, since each tree is mentioned in relation to two others. But I'm obviously not the arithmegician to figure it out.

And Ah Helped! ha!

If the oak tree was measured in relation to a second tree, we could figure this out with some trigonometry, but it's only related to the blue one. That means the oak is free to swing around the blue tree, and so the blue tree is free to swing around the pink one. So to speak...

I don't even know what trigonometry is, other than it's long for "trig", so I will defer to you on that but, I think the oak is just a red herring and doesn't mean anything. The relationship of the pink tree is given to both the orange and yellow one, so it has to have a set place somewhere, right?

Was this puzzle given to you on paper or orally, ear? I'm betting that something's been left out.

That sounds really funny put together that way.

[wintergreen48]

One of my fellow employees brought this to me - evidently it was a question at a Christmas party at her church. Although my math skills are fair, I can't seem to get a handle on the answer, so I figured I'd post it here.

In an open field there are 5 Christmas trees decorated with colors. The red Christmas tree and the orange Christmas tree are 10 yards apart. The yellow Christmas tree is 12 yards from the red Christmas tree. The blue Christmas tree is 14 yards from the oak tree. The pink Christmas tree is 17 yards from the blue Christmas tree. The yellow Christmas tree and the Orange Christmas tree are 9 yards apart. The yellow Christmas tree and the pink Christmas tree are 13 yards apart. The pink Christmas tree and the orange Christmas tree are 11 yards apart. How far is the blue Christmas tree from the red Christmas tree (rounded to the nearest yard)?

I don't think that you can solve this based upon the information that is given, perhaps something is missing? As given, the oak tree is a red herring, it does not give you anything really useful (unless one of the colored trees is actually the oak, which would be a weird choice of Christmas trees). The problem is that I think that I can see (at least) two different possible locations for the blue Christmas tree, which means that there at (at least) two different possible solutions for the distance between the red and the blue tree.

The way I see it, you have two different triangles, one is R-O-Y (Red tree to Orange tree then Orange tree to Yellow tree then Yellow tree back to Red tree), while the other is O-Y-P (Orange tree to Yellow tree then Yellow tree to Pink tree than Pink tree back to Orange tree). The two triangles have one common side, the line O-Y (Orange tree to Yellow tree). The reason for the (at least) two different possible solutions is that the Pink tree could be located on either side of the line O-Y. I will try to diagram it here:


Red Tree --------------10 yards --------- Orange Tree
| /
| /
| /
| /
| /
| /
| /
12 yards 9 yards
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
Yellow Tree

The Pink tree could be to the right of the O-Y line of the above triangle, which I think puts it something like 20 yards southeast of the Red tree. The Blue tree would be somewhere 17 yards away from the Pink tree-- in fact, the Blue tree would be in any one of an infinite number of locations on the perimeter of a circle that surrounds the Pink tree, that circle having a radius of 17 yards.

But the Pink tree could also be to the left of the O-Y line of the above triangle, which would put it very close to the Red tree, maybe a yard or above it. Again, the Blue tree would be somewhere 17 yards away from the Pink tree, again, in an infinite number of locations on the perimeter of a circle that surrounds the Pink tree in the new location, with that circle again having a radius of 17 yards.

So you have two completely different locations for the Pink tree, and the Blue tree can be in an infinite number of locations around each of the Pink tree locations, which makes it impossible to calculate.

Maybe this is a deliberately impossible puzzle? Or something is missing, that would connect the oak tree to the others, so that you could triangulate?

[MarleysGh0st]

I don't even know what trigonometry is, other than it's long for "trig", so I will defer to you on that but, I think the oak is just a red herring and doesn't mean anything. The relationship of the pink tree is given to both the orange and yellow one, so it has to have a set place somewhere, right?

Using those sines, cosines and tangents we learned back in high school, I think we have enough info to exactly measure the red, yellow, orange and pink trees with each other. But because the oak doesn't matter, we can only measure the blue with the pink. As I said, it can be anywhere on the circumference of a 17 yard circle around that one.

Was this puzzle given to you on paper or orally, ear? I'm betting that something's been left out.

That sounds really funny put together that way.

Yeah. Of course, when we abbreviate earendel's name, it's natural to pronounce it like the body part, but in Elvish it ought to be pronounced more like ee-are.

[fantine33]

Using those sines, cosines and tangents we learned back in high school,

You must be using the royal 'we'. I didn't have math in high school. I didn't even understand that otto has apples question in the qod the other day enough to get it once the answer was given.

I think we have enough info to exactly measure the red, yellow, orange and pink trees with each other. But because the oak doesn't matter, we can only measure the blue with the pink. As I said, it can be anywhere on the circumference of a 17 yard circle around that one.

Okay, then my first instinct was right. I only got confused when I went back and tried to read it correctly when I read your answer and saw I missed something. Who needs math when one has logic? Ha!

Yeah. Of course, when we abbreviate earendel's name, it's natural to pronounce it like the body part, but in Elvish it ought to be pronounced more like ee-are.

This frightens me more than the trigonometry cosine thingie.

[Bob78164]

If the oak tree was measured in relation to a second tree, we could figure this out with some trigonometry, but it's only related to the blue one.

I assume that one of the colored trees (not the blue or the pink, so the red, orange, or yellow) is the oak. But it seems as though any of the three candidates could be 14 yards from the blue tree, so I agree that we must be missing some information. --Bob

[Bob78164]

Unless there was some more information about the configuration of the trees, I'd say there's not enough information to solve this. Are they planted all in one line? In a square grid? The blue tree is only measured in relation to the pink one and to the oak, which isn't measured in relation to any other, so the blue tree could be anywhere in a 17 yard circle around the pink one.

Notwithstanding my earlier post, apparently someone thinks there's enough information to solve puzzle. --Bob

[earendel]

Oh, I totally missed the line about the pink and blue trees (I have reading issues). I think in that case there would be some way to figure it out, since each tree is mentioned in relation to two others. But I'm obviously not the arithmegician to figure it out.

And Ah Helped! ha!

If the oak tree was measured in relation to a second tree, we could figure this out with some trigonometry, but it's only related to the blue one. That means the oak is free to swing around the blue tree, and so the blue tree is free to swing around the pink one. So to speak...

Was this puzzle given to you on paper or orally, ear? I'm betting that something's been left out.

On paper - I typed it just as it appeared.

[earendel]

Suppose we replace the word "oak" with "orange" - the original puzzle just used "O.T." and somehow it got changed. Would that make a difference?

[Bob Juch]

Suppose we replace the word "oak" with "orange" - the original puzzle just used "O.T." and somehow it got changed. Would that make a difference?

Yes, then you'd have three connected triangles and can easily figure it out.

[NellyLunatic1980]

Suppose we replace the word "oak" with "orange" - the original puzzle just used "O.T." and somehow it got changed. Would that make a difference?

Yes, as it puts the blue tree in one definite position rather than any position that is 17 yards from the pink tree.

[MarleysGh0st]

Suppose we replace the word "oak" with "orange" - the original puzzle just used "O.T." and somehow it got changed. Would that make a difference?

D'oh!

Yes. Yes, it would.

[Bob Juch]

Suppose we replace the word "oak" with "orange" - the original puzzle just used "O.T." and somehow it got changed. Would that make a difference?

Yes, as it puts the blue tree in one definite position rather than any position that is 17 yards from the pink tree.

Actually you'd wind up with three triangles which could be on top of each other or the OPB one could be on top of just the OPY one, however the puzzler probably expected that would not be the case.

[earendel]

Suppose we replace the word "oak" with "orange" - the original puzzle just used "O.T." and somehow it got changed. Would that make a difference?

Yes, then you'd have three connected triangles and can easily figure it out.

So what's the answer, then?

[NellyLunatic1980]

So what's the answer, then?

21 yards. I'll give a detailed explanation later today.

[earendel]

So what's the answer, then?

21 yards. I'll give a detailed explanation later today.

Please do.

[andrewjackson]

Hmm. I get a bunch of different answers even if the oak tree is the orange tree.

The pink tree can be right next to the red one or 21 yards away. Which puts the blue one on a couple of different arcs that are varying distances from the red one.

I'll have to tackle this again later.

[fantine33]

If the OT/oak tree thing is right, that cracks me up. It's like a game of Telephone!

[andrewjackson]

I'm still getting at least four answers if "oak" is actually orange.

Start with a triangle with Yellow, Orange, and Pink at the corners and the correct number of yards apart.

Just for convenience let's say Yellow is to the West, Pink is due East of that, and Orange is to the North of them.

That would put the Red tree either off to the Northwest slightly over 20 yards from the Pink tree (R1) or inside the original triangle just about 1 yard to the west of the Pink Tree (R2).

The Blue tree would be off to the Northeast (B1) or down in the Southwest (B2).

That makes the distance from Red to Blue:

R1 to B1 - 20 yds
R1 to B2 - 15 yds
R2 to B1 - 17 yds
R2 to B2 - 16 yds

[andrewjackson]

BTW, if "oak" is not orange then the distance ranges from 4 yds to 38 yds.

[BackInTex]

I'm still getting at least four answers if "oak" is actually orange.

Start with a triangle with Yellow, Orange, and Pink at the corners and the correct number of yards apart.

Just for convenience let's say Yellow is to the West, Pink is due East of that, and Orange is to the North of them.

That would put the Red tree either off to the Northwest slightly over 20 yards from the Pink tree (R1) or inside the original triangle just about 1 yard to the west of the Pink Tree (R2).

The Blue tree would be off to the Northeast (B1) or down in the Southwest (B2).

That makes the distance from Red to Blue:

R1 to B1 - 20 yds
R1 to B2 - 15 yds
R2 to B1 - 17 yds
R2 to B2 - 16 yds

I agree there are 4 answers, but haven't done the math to get those answers.

T=Triangle
L=Line

T:POB joined T:POY on L:OP
T:POY joined to T:OYR on L:OY

There are two positions each join can have, flipping one of the triangles on the join line.

Two joins times two positions gives 4 locations for point B