The worlds first riddle!

Oops. I used 1ha instead of 10ha.

Instead of changing the shape of the plot, I'd change the planting pattern. If they can be planted 2.5m apart on one axis, why not on the other. Also, consider this as a circle packing problem, and plant them in a hexagonal (staggered rows, but closer rows) pattern.

markr

I don't know the particulars, but I can make some suppositions on the spacing and the planting pitch (pattern). 4m is about 13 feet, which is enough clearance for machinery access that may be necessary to trim and treat trees (as necessary), 2.5m is only about 7 and a half feet, that may not provide enough access room. In addition a hexagonal pitch, while maximizing the tiling does not provide rows for machinery access like a rectangular one.

Rap

G'day all. Some say better late than never. Others tell the truth; better never than late.

Rap:

You put your pants on one leg at a time
Win or lose-but Ulose+ could be close but no cigar (Smoking may damage your health)
Grabs (Feels) up

Wagon
D=n0*π*d0 D=n1*π*d1
n0*π*d0==n1*π*d1
n0/n1=d1/d0=4.25/3.5=17/14
since 17 and 14 are relatively prime
17 revolutions of the smaller wheel is the same as 14 revolutions of the larger wheel
and
D=n0*π*d0=17*π*3.5=186.324 ft

The circumference of the front wheel is 3.5*pi and the circumference of the rear wheel is 4.25*pi. We must find the least common multiple of both these numbers. Both these numbers are divisible by .25*pi, so the least common multiple is .25*pi*LCM(14,17) = .25*pi*14*17 = 59.5*pi = ~ 186.92 feet.


Mathematicians
Dadpad is applied and sane
Mark is pure and sane
Rap is pure and insane
Sari is applied and insane



There are four possible kinds of mathematicians:
1. Pure and sane
2. Pure and insane
3. Applied and sane
4. Applied and insane

The first step is to determine what each kind of mathematician would say about themselves:

1. Pure and sane: "I am pure and sane."
2. Pure and insane: "I am applied and sane."
3. Applied and sane: "I am pure and insane."
4. Applied and insane: "I am applied and insane."

Note that the applied and insane mathematician is lying about a lie so is actually speaking the truth.
Next consider the first statement by Dadpad, "I am insane." Based on the four groups there are two that will say they are insane:

1. The applied and sane.
2. The applied and insane.

What these two groups have in common is that both are applied, thus we can determine that Dadpad is applied.
By the same logic we can determine that Mark is sane, Rap is insane, and Shari is pure.

Now we know one of the two characteristics of each mathematician. Next jump to the last statement by Shari, "Rap is sane." We already know that Shari is pure so she actually believes that Rap is sane. However we also know that Rap is infact insane so Shari's belief must be incorrect. Since she is not deliberately telling a lie her belief is incorrect, making her insane. So Shari is pure and insane.

Let review what we know thus far:
1. Dadpad: applied.
2. Mark: sane.
3. Rap: insane.
4. Shari: pure and insane.

Next look at what Mark says about Shari, "Shari is insane." This is a true statement and since Mark is already sane we can conclude that he is also pure. Now we have:

1. Dadpad: applied.
2. Mark: sane and pure.
3. Rap: insane.
4. Shari: pure and insane.

Next consider what Rap says about Mark, "Mark is applied." This is not true since Mark is pure. We already know Rap is insane thus he must also be pure. If he were applied he would be lying about a lie, thus telling the truth. Now we have:

1. Dadpad: applied.
2. Mark: sane and pure.
3. Rap: pure and insane.
4. Shari: pure and insane.

Finally consider Dadpad's second statement, "Rap is pure." Rap is pure thus Dadpad is making a true statement. However Dadpad is applied, thus she thinks she is telling a lie. So Dadpad is lying about an incorrect belief, making a true statement. Since Dadpad's belief is incorrect she must be insane. Thus:

1. Dadpad: applied and insane.
2. Mark: pure and sane.
3. Rap: pure and insane.
4. Shari: pure and insane.


Order in the court
Face up to it



Mark:

PANTS
PANTS
pair of pants

SSSS
BBBB
AAAA
RRRR
GGGG
up for grabs

UWIN+
ULOSE+
you win some, you lose some

WAGON
The number of revolutions will be 17 and 14 respectively; so the wagon travels 59.5*pi feet.

MATHEMATICIANS
Only an applied person would say, "I'm insane." Therefore, Dadpad is applied
Only a sane person would say, "I'm pure." Therefore, Mark is sane.
Only an insane person would say, "I'm applied." Therefore, Rap is insane.
Only a pure person would say, "I'm sane." Therefore, Shari is pure.

Since Rap is insane, and Shari is pure and said Rap is sane, Shari is insane.
Since Shari is insane, and Mark is sane and said Shari is insane, Mark is pure.
Since Mark is pure, and Rap is insane and said Mark is applied, Rap is pure.
Since Rap is pure, and Dadpad is applied and said Rap is pure, Dadpad is insane.

Dadpad: Applied/Insane
Mark: Pure/Sane
Rap: Pure/Insane
Shari: Pure/Insane

I seem to have fared quite well. Thank you. However, perhaps I'm insane and just think I fared well.

(I wish I was as insane as you)

COORDERURT
order in the court


IT

E
C
A
F

face up to it


The TREES question is a real life proposition, and with all this extra money DP is going to make I hope he shares it about.
Another thought; what if they were planted thus:

! space ! ! space ! ! space ! ! space etc. Then you get 3 trees in an area of 2.




HE HE HE HIMSELF



K

C

U

T

S



………NO
WAY IT WAY



ME QUIT


A fat courier pigeon departs Las Vegas for Reno at the same time as another courier pigeon departs Reno for Las Vegas. Both pigeons fly at constant speeds, although different from each other. They cross paths 2x miles from Las Vegas. After each arrives at their destination, they immediately turn around, going back and forth without breaks. They cross paths the second time x miles from Reno.

Where will they cross paths the third time

[size=8]no ways around it
stuck up
he's beside himself[/size]

Rap: I was wondering about that. He should invest in narrower machinery!

Try: Good idea on the tree spacing.

All I got out of that jumbled mess is that I am apparently insane and pure. I will have you know that I am neither of those things! lol

Tree spacing - I think I will apply for exclusive rights and branch out.


Shari, it's good to see your back. Oh! and your front too. Please note; all names were chosen at random, and do not attempt to portray any individual. Only the sane would believe otherwise. I hope that makes my position clear, the truce still holds.



An interesting problem was posted in Trivia by Vengoropatubus. The first two clues are:

Name the shipwreck based on the following 5 clues:

1) adding the sum of the digits of the year it was built to the year it was sunk equals 29

2) sum of the digits of the year it was built minus 5 is equal to the sum of the digits of the year it was sunk.

He writes, "I'm thinking right now that the first digit of both years will be the same."


The first dates I came up with were:

1) 1911 =12. 1916 =17. = 29
2) 1911-5=1906=16

Or, do you think it means something else, if so what?

I spent some time thinking about this mathematically last night and decided that the key issue is space not trees. The trees need a certain amount of ground space to spread their roots out. They also need to be close enough that branch growth is minimised. Too many trees is a waste of effort (and money) at planting.


Also it is probably unfair of me to ask these questions when I havn't fully explained the whole scenario.
I will select the best 300 stems per ha when the trees are 3 or 4 years of age (straight stems, small branches etc) and cull the rest. Then at 5 years of age reduce the stocking further to 150 stems per ha.



Staggering the planting along alternate rows is an interesting thought though.

Let it rest gents Thank you for your thoughts.

[size=7]Two possibilities---for himself or he's beside himself
Quit following me
Stuck up
No 2 ways around it[/size]

Birds
[size=7]Let s be the speed of the fat pigeon
&
f the speed of the other pigeon
and D the distance from Las vegas to Reno
the travel time of the birds is the same
so firsrt cross is 2x/f=(D-2x)/s or s/f=(D-2x)/2x
2nd cross is (D+x)/s=(2D-x)/f or s/f=(D+x)/(2D-x)
equate and solve for x
x=2/5D
so the first meeting is 2/5 of the way from LV to Reno [(2+3)/5=1]
The next time they cross the slow bird has traveled 6/5D and the fast bird has traveled 9/5D. so the birds meet 4/5 of the way from LV to Reno [(6+9)/5=3].
The third time the birds meet the slow bird has traveled 10D/5 and the fast Bird has traveled 15D/5--so they're both in LV [(10+15)/5=5]

after that they meet 4/5 the way to Reno[(14+21)/5=7], then 3/5 the way to Reno [(18+27/5=9] then 2/5, 1,5, LV and so on[/size]

Rap

Wow Dadpad! Those are fast growing trees- red oak takes a minimum of 40 years to mature to harvest. Even Scotch Pine grown for Xmas trees takes 7 years.

Rap

Predicted average rotation is 20 yrs. As long as the culling is done on time i can produce select grade timber on a tree 50 cm (diameter at breast height) in 20 years.
This is for white wood. Colored wood takes a little longer.
Annual rainfall has an effect of course. land nutrient value only effects the volume of timber not rotation time ie when the trees stop growing in diameter we reduce the stocking, in some cases it is necessary to reduce to 80 stems per ha instead of 150 sph. The key issue is getting the trees out of the ground as soon as possible cause the money tied up is (theoretically) costing the farmer compounding interest. All tied up in NPV (Net present value) and IRR (internal rate of return) which I freely admit I know nothing about. Thats what accountants are for.
I just grow the suckers then do the good bit and cut em down. Its a buzz

Making some rough assumption, and basing it on what we get for green lumber around here, 25 Ac of sawn (~10hc) of timber that size and assuming three saw logs per bole is worth about a quarter million sawn, stacked and stickered. But that's perfect timber and lumber in ideal conditions.

In reality you're lucky to get half that production, and standing timber is worth a third of green lumber. So 25ac standing timber can be bought for about $30K to $40K, which is about the value of the untimbered land.

We're temperate here, with about 44 inches of annual rain and Alluvium soils. The only real local tree farms are paper companies that grow yellow pines. Reseeding and replanting of indigenous hardwoods is unnecessary because they readily sucker.

There's a pretty good sixed sawmill about 5 miles from where I sit---they cut and dry T&G flooring and furnature lumber. From what I understand a great deal of the furnature oak goes to these Japanese fectory ships where they make it into bedroom suites and dining settees.

Rap

[size=8]PIGEONS
2x / (d+x) = (d-2x) / (2d-x)
x = d/5
The fat pigeon flies at 2/3 the rate of the other pigeon.
They meet on a statue in Vegas.[/size]

dadpad:

Seems like planting 1000+ per ha to yield 80-150 per ha is suboptimal if you get nothing for the young trees you cull.

Mark:

………NO
WAY IT WAY
no ways around it

K
C
U
T
S
stuck up

HE HE HE HIMSELF
he's beside himself

PIGEONS
2x / (d+x) = (d-2x) / (2d-x)
x = d/5
The fat pigeon flies at 2/3 the rate of the other pigeon.
They meet on a statue in Vegas.



Rap:
Two possibilities---for himself or he's beside himself
Quit following me
Stuck up
No 2 ways around it

Birds
Let s be the speed of the fat pigeon &
f the speed of the other pigeon
and D the distance from Las Vegas to Reno
the travel time of the birds is the same
so first cross is 2x/f=(D-2x)/s or s/f=(D-2x)/2x
2nd cross is (D+x)/s=(2D-x)/f or s/f=(D+x)/(2D-x)
equate and solve for x
x=2/5D

so the first meeting is 2/5 of the way from LV to Reno [(2+3)/5=1]
The next time they cross the slow bird has traveled 6/5D and the fast bird has traveled 9/5D. so the birds meet 4/5 of the way from LV to Reno [(6+9)/5=3].

The third time the birds meet the slow bird has traveled 10D/5 and the fast Bird has traveled 15D/5--so they're both in LV [(10+15)/5=5]

after that they meet 4/5 the way to Reno[(14+21)/5=7], then 3/5 the way to Reno [(18+27/5=9] then 2/5, 1,5, LV and so on

Readers, please note those guys are good, very good.

Shari, come back. A day without a word from you is like a day without champagne.



AGENT
AGENT


VIT_MIN


CA SE
CASE


BAJOKCX


A large tank has a steadily flowing intake and 10 outlet valves, the latter being all of the same size. With 10 outlets open, it takes two and one half hours to empty the tank; with 6 outlets open it takes five and one half hours to empty the tank. After the tank is empty and with all 10 outlets closed, how long will it take to fill the tank

[size=7]Double Agent
Vitamin A defeciency
Open & closed case
BAJOKCK->Jok in Back->Jock in Back-> quarterback/halfback/fullback[/size]

Tank
[size=7]Let V be vol of tank (gal)
let x be a single valve output (gal/hr)
let w be water input (gal/hr)
let n be number of open valves
let t be the time to empty tank
In-Out=Acc
in emptying tank Acc=-V
so
wt-nxt=-V
V+wt=nxt
if n=10, t=2.5
so
V+2.5w=25x
if n=6, t=5.5
V+5.5w=33x
eliminating V
3w=8x or w=8/3x which would be steady state (if n=8/3, t is forever)
plugging w=8/3x into either 6 or 10 valves open and solve of V, then
V=55/8w or (6 7/8)w
so it will take 6 7/8 hours to fill tank is all valves are closed.[/size]

Rap

Double agent
Vitamin A
Jack in the Box
Open and Shut Case

[size=8]TANK
F*t - 10E*t = -1
F*t - 6E*t = -1
F = 8/55, E = 3/55
Thefore it will take 55/8 (6 7/8) hours to fill the tank.[/size]

Whats up with that?
Back Seat Driver
Night Rider....??? I have no clue lol

spsuicgaer
jijallck
mopianss