Some more
expensive, late model cars, have a pressure transducer in each wheel. This sends a signal to the main
computer which monitors the pressure and sends a signal to warn when tire
pressures become too low to be safe.
This signal is stored by
the computer and then read by the scan tool when a test or checkup is
done. Don.
-----Original
Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED]]On Behalf
Of Scott MacLean
Sent: Thursday, February 20, 2003
1:13 AM
To: MacLean List; Georgetown Crew
Mailing List
Subject: Puzzler of the week
This week's puzzler:
At our shop, we
have a scan tool. This scan tool is designed to plug in under the dash or
under the hood of the car and extract valuable information from the cars
computer.
Recently, we got a new piece of software for our scan tool. One of my guys had
plugged the scan tool in and was looking for readings that indicated a problem.
For example, if it says the engine operating temperature is minus 40 degrees,
you have some idea that theres something wrong with the engines temperature
sensor.
He was scrolling down and looking at all the information, when he came to a
reading that said, "air pressure low, right front tire."
He said, "Huh?!" So, I walked around to the right front tire and sure
enough -- the tire was almost flat. I said, "Its right."
The question is: How did the scanning tool know that the right front tire was
low on air?
Last week's puzzler:
This puzzle has been making the rounds of Hungarian mathematicians'
parties.
The warden meets with 23 new prisoners when they arrive. He tells them,
"You may meet today and plan a strategy. But after today, you will
be in isolated cells and will have no communication with one another.
"In the prison is a switch room, which contains two light switches labeled
A and B, each of which can be in either the on or the off position. I am
not telling you their present positions. The switches are not connected
to anything.
"After today, from time to time whenever I feel so inclined, I will select
one prisoner at random and escort him to the switch room. This prisoner
will select one of the two switches and reverse its position. He must move one,
but only one of the switches. He can't move both but he can't move none
either. Then he'll be led back to his cell.
"No one else will enter the switch room until I lead the next prisoner
there, and he'll be instructed to do the same thing. I'm going to choose
prisoners at random. I may choose the same guy three times in a row, or I
may jump around and come back.
"But, given enough time, everyone will eventually visit the switch room as
many times as everyone else. At any time anyone of you may declare to me,
'We have all visited the switch room.'
"If it is true, then you will all be set free. If it is false, and
somebody has not yet visited the switch room, you will be fed to the
alligators."
Here's the question:
What is the strategy the prisoners devise?
Last week's puzzler answer:
The prisoners all meet, and the leader of the prisoners says,
"Okay, guys, here's our strategy. First, there's only one guy who can
count past two, so we're naming him 'The Counter.' He's going to be responsible
for telling the warden we've all been in the switch room when the time comes."
He then proceeds to give instructions to the other inmates. He says,
"We're going to designate Switch A -- the switch on the left - as the
"real switch." That's the only switch that matters to The Counter.
The other switch, Switch B, is a dummy. It won't tell us anything, and you just
use it when you have to move a switch, but don't want to move Switch A. You got
it? So Switch A is the meaningful switch and Switch B is a placeholder."
So, each of the 22 prisoners is told, "When you go into the switch room,
we want you to move Switch A to the "On" position. If Switch A is
already in the "On" position, then leave it there, flick switch B and
walk out." All the prisoners nod.
Now I want each of you to flick Switch A to the "On" position twice,
and only twice. So if you go in there and Switch A is already on, that doesn't
count. I want each of you to actually flick it "On" two times. You
got that? "
All the prisoners nod. One of them raises his hand, tentatively.
"Yes, Berman?"
"Who's going to be flicking Switch A off, he asks.
"Good question," says the leader. "The Counter is the only one
with the authority to turn off Switch A."
So, each time The Counter is taken into the switch room, finds the switch in
the "On" position, he knows that at least one prisoner has been in
there.
It could be one prisoner who came in and turned it on, or it could be six
prisoners -- the first one turning it on and the next five leaving it on. But
when The Counter walks in and finds Switch A in the "On" position, he
knows at least one prisoner has been in the room since the last time The
Counter turned the switch off.
And when you work it all out, The Counter has to turn off Switch A 44 times in
order to know that all 23 prisoners have been in the switch room. And the reason
he has to count that high is that he doesn't know what the original position of
the switch is, and therefore he has to wait for everyone to go in twice.
In other words, if the warden started with Switch A in the "On"
position, and The Counter was brought in first, he could be fooled into
thinking that another prisoner had been in there. And that's why it's 44
instead of 22. .
If you have trouble understanding the strategy, try it for two prisoners --
Prisoner 1 and Prisoner 2.
Let's say Prisoner 2 is The Counter. Prisoner 1 is brought in first. He sees
Switch A is in the "Off" position, so he flicks it on. Let's say
Prisoner 1 is brought in again. Remember -- the warden picks prisoners
randomly. So Prisoner 1 leaves Switch A on and flicks Switch B, which doesn't
matter. At some point, The Counter comes in, finds Switch A on and flips it
off. That's once, he says. Eventually, Prisoner 1 is brought back in, and he
turns Switch A on again. When Prisoner 2 comes back, he sees Switch A on, and
now he knows that the other prisoner has been there. Last time he was there, he
personally turned off Switch A, and now it's back on, so he knows the other
prisoner did it, and he says, "Warden, our work here is done."
And interestingly, the number of times The Counter has to turn Switch A off is
exactly twice the number of the other prisoners -- not counting him -- in the
group. So, for two prisoners, it's two times. For 23 prisoners, it's 44 times.
_______________________
Scott MacLean
[EMAIL PROTECTED]
ICQ: 9184011
http://www.nerosoft.com
