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New Business Opportunity – Make Money Fast

Posted by Karl Sharman on August 7, 2010 – 9:16 am

You have just started up your new business, producing Numples.

The process for producing numples is fairly easy, but the procedure and sequence for operating the equipment takes precision timing and materials that need to be added and used at very specific intervals to keep things going and numples producing.
You produce numples in a system using 5 stages. Your system requires, occurring in this order, a coolant, a lubricant, a catalyst coating, and the secret numple ingredient. Once all these are complete, the system moulds and presses out a single numple.

Given the following requirements for your system’s equipment, how long does it take to make a single numple?

A) During any of the 5 stages, only that process can occur. This means that when lubricant is being added, nothing else can occur. When a numple is being pressed, no coolant can be added, etc.
B) The coolant must be added within every 2 minutes, otherwise the reactor will overheat. It takes a full minute to add the coolant and it must be added uninterrupted.
C) The lubricant must be added within every 10 minutes, otherwise the reactor will lock up. It takes 2 minutes to completely add lubricant needed for the catalyst stage.
D) A full sample of catalyst coating must be added to the reactor before any numple material can be added. Catalyst material only lasts for 50 minutes before dissolving. It takes 10 minutes total to add the needed coating.
E) Numple material takes 8 minutes to add.
F) Pressing and moulding a numple takes 2 minutes.

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12 Responds so far- Add one»

  1. 1. forsythe303 Said:

    My guess is 42 minutes (as outlined below):

    ACTIVITY TOTAL
    TIME TIME
    —- —-
    Add Coolant 1 1
    Add Lubricant 2 3
    Add Coolant 1 4
    Add 20% of Catalyst 2 6
    Add Coolant 1 7
    Add 20% of Catalyst 2 9
    Add Coolant 1 10
    Add 20% of Catalyst 2 12
    Add Coolant 1 13
    Add Lubricant 2 15
    Add Coolant 1 16
    Add 20% of Catalyst 2 18
    Add Coolant 1 19
    Add 20% of Catalyst 2 21
    Add Coolant 1 22
    Add Secret Ingredient 2 24
    Add Coolant 1 25
    Add Lubricant 2 27
    Add Coolant 1 28
    Add Secret Ingredient 2 30
    Add Coolant 1 31
    Add Secret Ingredient 2 33
    Add Coolant 1 34
    Add Secret Ingredient 2 36
    Add Coolant 1 37
    Add Lubricant 2 39
    Add Coolant 1 40
    Mold Numple 2 42

    So the first numple takes 42 minutes.

  2. 2. Nathan Said:

    48 min

    a unit of coolant needs to be added every other minute.
    of the remaining time, two consecutive openings need the lubricant, and they need to occur every two minutes. of the remaining time, the catalyst material is added, followed by the numple material. once all the material is added, the pressing and molding occurs. visually, this looks like the following

    C L C L C A C A C A C L C L C A C A C N C L C L C N C N C N C L C L C N C N C N C L C L C N P

    where C is coolant, L is lubricant, A is catalyst, N is numple material, and P is pressing and molding.

  3. 3. Karl Sharman Said:

    Nope and Nope.

  4. 4. Eketahuna Said:

    60 minutes per Numple

  5. 5. Eketahuna Said:

    Strike that, I forgot about the catalyst only lasting 50 minutes :(

  6. 6. Eketahuna Said:

    Hmm, it all depends on some of the criteria, but all the Numple is added before the 50 mins is up, so I’ll stick with the 60 minutes :-)

  7. 7. slavy Said:

    There might be a good chance that I haven’t understood the problem completely, but I have 2 guesses.

    The first one is: the hell with all the equipment – I don’t need it forever and I am asked to make only a single Numple, so I will just do the procedures in the correct order and let the coolant reactor overheat and the lubricant one lock up :) This apocalyptic strategy will cost me 23 minutes and I will be pronounced the fastest Numple guy ever! Of course, I will be fired immediately after that.

    If we care about the equipment, then I would guess 52 minutes are necessary. There is no point to have two consecutive 1s (I denote the 5 stages with 1,2,3,4 and 5 respectively) since only 1 minute of material 1 is needed, so everything else just keeps the reactor alive. And since we have to start with adding 1, it follows that all the odd minutes should be occupied with this procedure. So from now on we can just consider the even minutes. With this restriction, the time for each of the procedures remains the same, but 2 should be added within every 5 operations. In the problem it was written that we cannot mix stages, so we have to start with 2 2s and then we just add the necessary amount of 3s and 4s and 5s. The total minutes for the last three stages needed is 20, so in between we need 20:5=4 additional 2s. So, we need at least 2+20+4=26 even minutes, and thus, 2*26=52 minutes in total.

  8. 8. forsythe303 Said:

    57 minutes

    Borrowing from Nathan’s lettering system and adding a few of my my own:

    C = Coolant
    hL = Half Lubricant
    tA = One-Tenth of the Catalyst
    eS = One-Eighth of the Secret Ingredient
    hP = One-Half of the Pressing and Molding

    Everything has to be broken down into one minute intervals as has been previously pointed out, the C must be added every other minute. Here’s the answer I have come up with (after spending quite some time developing a spreadsheet with nifty formulas for keeping track of how long it has been since the material was last added, the total time, and when I should add any particular material. Thanks Karl for keeping my spreadsheet skills in practice.

    C
    hL
    C
    hL
    C
    tA
    C
    tA
    C
    hL
    C
    tA
    C
    tA
    C
    tA
    C
    hL
    C
    tA
    C
    tA
    C
    tA
    C
    L
    C
    tA
    C
    tA
    C
    eS
    C
    eS
    C
    L
    C
    eS
    C
    eS
    C
    eS
    C
    eS
    C
    L
    C
    eS
    C
    eS
    C
    hP
    C
    hP

  9. 9. Jhowmar Said:

    The machine will blow up before you get the first one out

    A) During any of the 5 stages, only that process can occur. This means that when lubricant is being added, nothing else can occur. When a numple is being pressed, no coolant can be added, etc.

    how do you

    B) The coolant must be added within every 2 minutes, otherwise the reactor will overheat. It takes a full minute to add the coolant and it must be added uninterrupted.

    in the middle of

    D) A full sample of catalyst coating must be added to the reactor before any numple material can be added. Catalyst material only lasts for 50 minutes before dissolving. It takes 10 minutes total to add the needed coating.

    with out breaking rule A

  10. 10. Jhowmar Said:

    ok well reading other posts yea it doesn’t say you can’t stop a process so as long as you can intrupt the nurple pressing

    forth looks like he’s gettin close

    C
    hL
    C
    hL<— start 10 min counter
    C
    tA
    C
    tA
    C
    hL
    C
    tA
    C
    tA<—- lub should probally be fully re inserted by now
    C
    tA
    C
    hL<— need to move up

    I think it's gonna be just a little off for the fact of the the prior requirments will probally need to be fully inserted before they wear off for the next step

    to lazy to figure it out that way though

  11. 11. Karl Sharman Said:

    The published answer for solving this is to use Excel and fill in each block as one minute of each process that needs to occur next.

    1) The coolant will need to be added every other minute by definition. (i.e. 1,3,5,7,etc, all odd minutes, are always coolant only)

    2) The lubricant can be fully added by minute 4 using minutes 2 and 4. Since it needs to be added every 10 minutes, lubricant will always be minutes 2,4….12,14….22,24….32,34, etc.

    3) The catalyst can be started by minute 6, but won’t end until minute 36

    4) Now you can add numple material, but only 5 of 8 minutes worth before you need to add another full sample of catalyst.

    5) Nicely enough the pattern works the same for the next 50 minutes except since you only need 3 more units of numple material, you have 2 minutes of spare time at minutes 98 and 100 to press and mould the numple.

    Therefore it takes 100 minutes to make one numple!

  12. 12. cazayoux Said:

    I agree it takes 100 minutes, but I’ve got a different order than KS.
    Coolant every odd (1,3,5,…) (1 minute of 2)
    Lubricant the next two available slots every 10 slots (2,4,12,14,22,24, … ,92,94) (2 minutes every 10)
    Coating the next two available slots every 10 slotes (6,8,16,18,26,28,36,38,46,48 and 56,58…,96,98) (10 minutes every 50)
    Secret Ingredient the last available slot every 10 slots for 8 separate slots (10,20,30,…80) (8 minutes every 100)
    Press the last available slot in the last two 10-minute segments (90,100) (2 minutes every 100)

    The first eight 10-minute segments:
    Coolant
    Lubricant
    Coolant
    Lubricant
    Coolant
    Coating
    Coolant
    Coating
    Coolant
    Secret

    The next two 10-minute segments:
    Coolant
    Lubricant
    Coolant
    Lubricant
    Coolant
    Coating
    Coolant
    Coating
    Coolant
    Press

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