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## Busy Break Room

Posted by DP on December 22, 2010 – 8:36 am

It’s lunch time in the office, and people are getting hungry. Let’s say most people bring their food to work, keep it in the refrigerator, and microwave it around noon. There is a hallway outside the break room that can hold a large amount of people. At 12:00:00 the office employees may take their lunch break. Figure out the maximum amount of people that could enter and exit the room by 12:15:00 using the following rules:
1) it takes 5 seconds to walk to the fridge and get out food
2) since there is only 1 refrigerator, you cannot enter the room until the person before you is done at the fridge
3) it takes 1 minute, 20 seconds to microwave the food
4) there are only 3 microwaves, and you cannot share
5) it takes 15 seconds to finish preparation in the break room after heating up the food (get plates, napkins, forks, season your food, get some coffee…)
6) fire code says a maximum of 4 people may be in the room at any given time
Let’s also assume an empty room at noon.

This post is under “Logic, MathsChallenge, Tom” and has 13 respond so far.

### 13 Responds so far- Add one»

1. 1. Becca Said：

is it 33 people enter, 29 people exit, and 4 people are in the room still at 12:15.

2. 2. Ashish Said：

My calculations says at end of 12:15:00

117 people would have gone through the room.
and 4 people will be inside the room.

This is the answer i got in first go…will verify the method again to see if it is really an answer.

3. 3. cazayoux Said：

Consider 5 second increments, F = Fridge, M = Microwave, P = Prep

F MMMM MMMM MMMM MMMM PPPf mmmm mmmm mmmm mmmm pppF MMM
. …F MMMM MMMM MMMM MMMM PPPf mmmm mmmm mmmm mmmm ppp
. …. …F MMMM MMMM MMMM MMMM PPPf mmmm mmmm mmmm mmm
. …. …. …. …F MMMM MMMM MMMM MMMM PPPf mmmm mmm

It takes 140 seconds for the first three people to finish.
It takes 80 more seconds for the next four people to finish

15 minutes = 900 seconds
(900 – 140) / 80 = 9, remainder 40 seconds
In that remaining 40 seconds, one more person can finish.

3 (first full set) + 3*9 (next full sets) + 1 = 31 people

4. 4. cazayoux Said：

sorry … font kept formatting from looking good.
(need Courier)

F MMMM MMMM MMMM MMMM PPPF MMMM MMMM MMMM MMMM PPPF MMM
_ ___F MMMM MMMM MMMM MMMM PPPf mmmm mmmm mmmm mmmm ppp
_ ____ ___F MMMM MMMM MMMM MMMM PPPf mmmm mmmm mmmm mmm
_ ____ ____ ____ ___F MMMM MMMM MMMM MMMM PPPf mmmm mmm

5. 5. Dual Aspect Said：

Agree with cazayoux; I make it 31 too.

6. 6. DP Said：

Ashish, I will say this…even if all four people were allowed in the room at one time, and there were four microwaves, there could only be 36 people.
5 sec + 80 sec + 15 sec = 100 sec
15 min * 60 sec = 900 sec
900 / 100 = 9 cycles of people
9 * 4 people = 36 total

This is not the answer, but i am simply proving that 117 is a little high. how did you come up with that answer?

Becca was close, but cazayoux got it correct.

I’ll let some others post their methods (or just let some time pass) before i post my solution.

7. 7. Ashish Said：

Hey DP,

Well i was working on some assignment and simultaneously solving the puzzle as well thus missed on 1 min 20 sec microwave part. Ohh may be that is why my lunch is always cold .
In my ignorance i assumed that it takes 5 sec to walk to fridge, 15 sec for microwave, restriction on sharing microwave and fire code.

Made a pattern again for correct timings and it is coming out what cazayoux suggested… 31 .

8. 8. DP Said：

Looks good. Cazayoux was incorrect in saying the first three people take 140 secs. It would actually be 110 for the first three.
Good job on noticing the microwave being the main limiting factor. There can be four people in the room but one may end up standing around until a microwave is free.

9. 9. Al Gelman Said：

I agree that 31 is the correct answer, but I’m afraid I do not understand Cazayoux’s analysis at all, especially since he used 140 sec. for three to complete instead of 110.
Anyways, here is another solution. As noted by DP, the line up at the microwaves is the determining factor. But because of the timing, there is a line only at microwave no. 1. Numbers 2 and 3 are always free for the next person. Now the first person is done with the microwave after 85 seconds. Waiting for his turn, is person number 4. No. 4 is finished in 85 + 80 = 165 sec. Following him is person number 7 who finishes at 165 + 80 = 245 sec. And so on. Therefore we have 85 + 80X = 885 (because we need an additional 15 sec to exit the room). Where X, is the unknown number of groups of three that can be accommodated. 80X = 800, and X=10 groups of three. Therefore 10×3 =30 persons + the first. And the answer is 31.

10. 10. DP Said：

Al, sorry for the delay in responding. Christmas can take up a person’s time.
Yes. That is a pretty sound method of solving the problem. to be honest, I first solved the problem similarly to cazayoux where I let a letter represent 5 seconds at each of the three stages. I lined them up (vertically in my method) to solve the problem.
Your mathematical representation is much neater/cleaner and should be the way I will attempt my own problems from here forward.

11. 11. DP Said：

Ashish, I can see how you were mistaken and assume you were on track in your thinking. partial credit awarded.
Dual Aspect, while no work was shown, i can only assume you solved it similarly to my own and cazayoux’s method. However, you didn’t point out his 140 second mistake.
cazayoux gets full credit for getting the correct answer and solving it the same way i did, with the side note to correct the time of the first 3 people.
Al gets full credit for nicest solution and a correct answer.
Still haven’t heard from Becca.

12. 12. ankur Said：

well to my calculation 27 people enters the room and 24 exits the room in 15 min.

13. 13. DP Said：

@ ankur: how did you come up with that answer?
a few of us came up with 31. see post #3 and #9 for two methods of solving.

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