Ask a Slacker: Logic Problems
Three men go to a hotel (nothing kinky) and each pay $10 for a $30 room. The manager feels bad about all three men staying in one room, and he tells the bellhop to give back $5 to the guys. The bellhop decides that it was too difficult to break a five dollar bill, so he gives each of them a dollar. That would make the initial investment $9 each, times 3 guys, is $27. What happened to the other $3?
The hotel got it. This is a weirdly worded version of a pretty basic question. You could ask it like this: Three guys rent a room (still nothing kinky) for thirty bucks. The manager says, "Hey we gave em the room with the dead racoons in the bathtub (no rub-a-dub for them that night), lets give em each a buck back."
The manager got $30 originally minus the three is $27. The thrifty threesome spent nine bucks each. That five dollar stuff is just thrown in to make it sound confusing.
"Whoops!" said Jimbo! "I forget my locker combination again."
"Relax," said Emily. "What do you remember about it?"
"Well, as you know, each of the three numbers of my combination can be anywhere between 1 and 39 inclusive. I do remember each one was different and the sum of the first two numbers was 42."
"Okay, what else?"
"And the last two numbers differed by only two. Oh yes, and all three numbers were primes."
"Well Jimbo, it just so happens that I actually remember your combination. But since you think you're so smart, I'll only give you one hint. If you take the three numbers of your combination and multiply them together, the last digit of the product will be...." And Kyle whispered something in his ear.
With that, Jimbo was able to deduce his combination and open his locker.
What was his combination?
Whew, that's a good one. Let's dive right in, shall we?
First, we need to sort out the information that the question gives us. The three numbers are all between 1 and 39, each one is different, and the sum of the first two is 42. Also, the last two numbers differed by two, and all three numbers are primes. We also find out one more thing. Emily knows what the last digit in the product of the combinations is. Why is that important? Read on...
Lets start with the first hint, that the first two numbers in the combonation add up to 42. This gives us quite a few choices, but remember, all of the digits are primes, and they are between 1 and 39. That gives us the following options:
5 + 37 = 42
11 + 31 = 42
13 + 29 = 42
23 + 19 = 42
29 + 13 = 42
31 + 11 = 42
37 + 5 = 42
41 + 1 = 42Okay, so far so good, right? Let's add the last number in now. Remember that the third number will differ from the second number by two. Also note that each of the above possibilities is listed twice below, one for the possibility that the third number is two higher than the second, and one for the chance that it's two lower.
05 37 35
05 37 39
11 31 29
11 31 33
13 29 27
13 29 31
23 19 17
23 19 21
29 13 11
29 13 15
31 11 09
31 11 13
37 05 03
37 05 07
41 01 03Down to 17 choices, not too shabby! Don't worry, we get to knock a few more of those out now. Remember, all three numbers have to be prime. Let's dump the ones that aren't...
11 31 29
13 29 31
23 19 17
29 13 11
31 11 13
37 05 03
37 05 07That's a bit cleaner, but we're not quite there. Remember Emily's hint? "If you take the three numbers of your combination and multiply them together, the last digit of the product will be...."
It seems insignificant, but lets check it out:
11 31 29 --> 9
13 29 31 --> 7
23 19 17 --> 9
29 13 11 --> 7
31 11 13 --> 3
37 05 03 --> 5
37 05 07 --> 5Still with me? We're almost done. We now know that Emily whispered one of only four numbers to our forgetful friend Jimbo: 3, 5, 7, or 9. However, we also know that this was enough information for Jimbo to figure it out. That's all we need to know, too. Emily whispered the number 3, and Jimbo's combination is 31 11 13. How do we know? Because if she would have told him 5, 7, or 9, he wouldn't have had enough information. There are two choices for each of those numbers. Hopefully Jim will write down his combination this time.
A group of soldiers were standing in the blistering sun facing due west. Their sergeant shouted at them:
Right turn!
About turn!
Left turn!
In which direction are the soldiers now facing????
I sincerely hope this isn't one of those questions that look easy then you say, "did I mention the soldiers are standing in a metal orb floating through space?" I hate those.
Anyway taken at face value the soldiers and assuming that 'turn' is like 'face,' meaning to turn 90 degrees (how do you make that little symbol?) in whatever direction, they would be facing East.
Their right turn would point them North, the about face would have them looking South, and the final left would point them East.
That reminds me of a Gomer Pyle episode I saw the other day. Which one was that were Gomer ticked off Sgt. Carter???
Thanks to George, Tampax Jones, and Melanie for the questions. You have a stumper? Send it on in!