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