Brain Quiz #17

Okay, I bought the Die Hard Trilogy the other day, so this is in honor of that. We’ve got a number of so called “Overspill” problems, then a timing one I really liked (and struggled with for a while, because my brain is damaged.) The overspills are worth 3 points, and the timing one is 5.. so you can pick up 20 points here, or 25 if you’re first.

Overspill problems

  1. You have a 5 gallon bucket and a 3 gallon bucket. Unlimited water supply. Measure exactly 4 gallons. [If you are wrong, the bomb will explode.]
  2. You have a 9 gallon bucket and a 4 gallon bucket. Unlimited water supply. Measure exactly 6 gallons.
  3. You have a 4 gallon bucket and a 5 gallon bucket. Unlimited water supply. Measure exactly 2 gallons.
  4. You have a 7 gallon bucket, a 4 gallon bucket, and a 3 gallon bucket. The 7 gallon bucket is full. You have no extra water. You must end up with exactly 2 gallons in two of the buckets and 3 gallons in the remaining bucket.
  5. You have an 8 gallon bucket filled with 5 gallons of water, a 5 gallon bucket filled with 3 gallons of water, and a 3 gallon bucket filled with 2 gallons of water. In two “moves”, how can you end up with exactly 1 gallon in one of the buckets?

Timing Problem

You have a 7 minute sandglass, and a 4 minute sandglass. How can you accurately measure 9 minutes?

25 thoughts on “Brain Quiz #17

  1. 1.
    fill the 3 gb
    pour that into the 5 gb
    refill the 3 gb and top off the 5 gb
    empty the 5 gb, and pour in the remaining 1 gallon from the 3 gb
    refill the 3 gb and dump it in the 5 gb

    2.
    fill the 9 gb.
    pour out 4 gallons into the 4gb.
    empty the 4gb and pour out 4 more gallons, leaving you with 1 in the 9 gb.
    empty the 4 gb, and pour the single gallon from the 9gb into it.
    fill the 9gb, top off the 4gb. this leaves you with 6 gallons in the 9gb.
    3.
    fill the 5gb, pour into the 4gb.
    empty the 4gb, pour the 1gallon into the 4gb
    fill the 5gb, top off the 4gb.
    leaves you with 2gallons in the 5gb.
    4.
    fill 3gb, pour that into 4gb (4 3 0)
    fill 3gb, top off 4gb (1 4 2)
    dump 4gb into 7gb (5 0 2)
    dump 3gb into 4gb (5 2 0)
    fill 3gb with 7 gb (2 2 3)
    5.
    top off 3gb with 8gb (4 3 3)
    top off 5gb with 3 gb (4 5 1)
    timing.
    measure 4 min off the 7ms (4-3)(4-0)
    measure 3 min off the 4ms (7-0)(1-3)
    measure 1 min off the 7ms (6-1)(4-0)
    measure 4 min off the 6minute side of the 7ms (2-5) (4-0)
    run 5minutes then 4minutes for 9 minutes.

  2. Timing problem….
    flip both timers over, when the 4min timer is done flip it back over. when the 7 min timer is done flip it over again also. (7 min.) when the 4 timer is done it will be 8 min. then flip the 7 timer over before it’s done. there should be one min of sand in the 7 timer and when it’s done that will equal 9 min.

  3. 1. Fill 5 (5, 0). pour 5 into 3 (2, 3). empty 3 (2, 0). pour 5 into 3 (0, 2). Fill 5 (5, 2). pour 5 into 3 (4, 3). empty 3 (4, 0).

    2. Fill 9 (9, 0). pour 9 into 4 (5, 4). empty 4 (5, 0). pour 9 into 4 (1, 4). empty 4 (1, 0). pour 9 into 4 (0, 1). fill 9 (9, 1). pour 9 into 4 (6, 4). empty 4 (6, 0).

    3. Fill 5 (5, 0). pour 5 into 4 (1, 4). empty 4
    (1, 0). pour 5 into 4 (0, 1). fill 5 (5, 1). pour 5 into 4 (2, 4). Empty 4 (2, 0).

    4. (7, 0, 0). Pour 7 into 4 (3, 4, 0). pour 4 into 3 (3, 1, 3). Pour 3 into 7 (6, 1, 0). pour 4 into 3 (6, 0, 1). pour 7 into 4 (2, 4, 1). pour 4 into 3 (2, 2, 3).

    5. (5, 3, 2). 1. pour 8 into 3 (4, 3, 3). 2. pour 3 into 5 (4, 5, 1).

  4. Does “measure” in the first three mean you have to end up with that much in one of the buckets, or does the measured water go somewhere else, so you can say “that was x gallons” and it doesn’t matter how much is left in the buckets?

  5. Ok, I’m assuming that the answer to my question will be yes, and also (for #2) that you’re allowed to spill water that doesn’t count toward your measurement.

    1. Fill the 5-gal bucket and pour it into the 3-gal bucket. 2 gallons overflow. Pour the 3 gallons back into the 5-gal bucket and top it off. Pour the 5 gallons into the 3-gal bucket. 2 more gallons overflow, so 4 in all.

    2. Fill the 4-gal bucket and pour it into the 9-gal bucket three times. 3 gallons overflow. Dump out the 9 gallons and repeat the process. 3 more overflow, for 6 total.
    Note to Answer Man: if this dumping isn’t allowed, please include that in your answer to my other question.

    3. Dump the 5-gal bucket into the 4-gal bucket; 1 gallon overflows. Dump the four gallons back into the 5-gal bucket, then top it off and pour it into the 4-gal bucket again; another gallon overflows, for a total of 2.

    4. I don’t know if this is the most efficient way, but it seems to work:
    Fill the 3-gal bucket from the 7-gal (4/7, 0/4, 3/3)
    Pour the 3-gal into the 4-gal (4/7, 3/4, 0/3)
    Fill the 3-gal from the 7-gal (1/7, 3/4, 3/3)
    Fill the 4-gal from the 3-gal (1/7, 4/4, 2/3)
    Pour the 4-gal into the 7-gal (5/7, 0/4, 2/3)
    Pour the 3-gal into the 4-gal (5/7, 2/4, 0/3)
    Fill the 3-gal from the 7-gal (2/7, 2/4, 3/3)

    5. Pour the 5 gallons from the 8-gal bucket into the 3-gal bucket. Pour the three gallons from the 3-gal bucket into the 5-gal bucket, catching the overflow in the 8-gal bucket. The 8-gal bucket now contains 1 gallon.

    Timing problem:
    Start both.
    When the 4-min one finishes, flip it.
    When the 7-min one finishes, flip it.
    When the 4-min one finishes, flip it.
    When the 4-min one finishes, flip it.
    When the 7-min one finishes, turn the 4-min one on its side to stop it. It now contains 2 minutes worth of sand, so running it and the 7-min one sequentially will take 9 minutes.

  6. “Measure” means at the end, that amount should be stored in one of the available buckets. The amount of water spilled out, if any, does not count towards your goal.

  7. Yeah, I should have gotten that. Especially since it turns out to be not that much harder.
    Revised answers:
    1. Fill the 3-gal and pour it into the 5-gal. Do so again, but only until the 5-gal is full. Dump out the 5-gal and pour the remaining gallon from the 3-gal into it. Fill the 3-gal and pour it into the 5-gal, which now contains 4 gallons.

    2. Fill the 9-gal and fill the 4-gal twice from it, then empty the 4-gal again and pour the remaining 1 gallon from the 9-gal into the 4-gal. Fill the 9-gal again and top off the 4-gal from it. 6 gallons are left in the 9-gal.

    3. Fill the 5-gal, then fill the 4-gal from it. Dump the 4-gal and put the 1 gallon from the 5-gal into it. Fill the 5-gal and top off the 4-gal from it. The 5-gal now contains 2 gallons.

  8. #1. Fill both the 5 gallon bucket and the 3 gallon bucket with water. Put the 3 gal. in the 5 gal. and what is left when you pull out the 3 gal should be 2 gallons. Next, empty the 3 gal, and pour the remaining 2 gal from the 5 into the 3 gal. and cover it in some way sono water can go in or out. fill the5gallon again and put the 3 in the 5 , this will once again leave 2 in the 5, now pour the 2 gallons from the first time back in the five gallon with the remaining 2 in the five gallon bucket, this leaves you with exactly 4 gallons of water.

  9. Timing Problem
    Flip both over, when the 4 runs out flip it over, when the 7 runs out flip it over, when the 4 runs out again, flip the 7 over again. When the 7 runs out, which only had one this last time, you will be at 9 minutes.

  10. Overspills:
    (I’m gonna call buckets by their sizes…)
    1. Fill 3, dump into 5. Fill 3, use to fill 5 to top. Empty 5. Pour remaining contents of 3 into 5. Fill 3, dump into 5. Leaves no water in 3, and 4 gallons in 5.

    2. Fill 4, dump into 9. Fill 4, dump into 9. Fill 4, use to top off 9. Empty 9. Pour remaining contents of 4 into 9. Fill 4, dump into 9. Fill 4, use to top off 9. Empty 9. Pour remaining contents of 4 into 9. Fill 4, pour into 9. Leaves no water in 4, 6 gallons in 9.

    3. Fill 4, dump into 5. Fill 4, use to top off 5. Empty 5. Pour remaining contents of 4 into 5. Fill 4, use to top off 5. Leaves 2 gallons in 4 and 5 gallons in 5.

    4. Fill 3 with water from 7. Pour 3 into 4. Fill 3 with water from 7. Top 4 off with water from 3. Pour 4 into 7. Pour 3 into 4. Fill 3 with water from 7. Leaves 2 gallons in 7, 2 gallons in 4 and 3 gallons in 3.

    5. Top off 3 with water from 8. Top off 5 with water from 3. Leaves 1 gallon in 3, 4 gallons in 8 and 5 gallons in 5.

    Timing:
    Prep: Turn both sandglasses over. When 4 minute runs out, immediately turn it over again. When 7 runs out, turn it over immediately. When 4 runs out, turn it over again. Wait till 4 runs out again.
    Start: When prep is completed, immediately start timing of 9 minutes. After 7 runs out (which will be after 2 minutes), turn 7 over again, and 9 minutes will be when 7 runs out again.

  11. What kind of bomb is triggered with water? If there’s so much water, I’d be pretty sure there’d be a pelican around. I’d make the bomb look like a fish, the pelican would eat it, and then I’d scare it away.

    It’s still less circuitous than all that measuring.

    ** licks finger, makes imaginary ‘point’ on the chalkboard

  12. For the time one. You start both 4 minute and 7 minute at the same time. Once 4 minute timer is up. You immediately flip it over again. Once 7 minute is up, you flip that over again immediately.

    Right now there should be one minute left in 4 minute timer. And the 7 minute timer is filling up at the bottom. Once the 4 minute timer gets done for the second time, you’re at the 8 minute marker with 1 minute of sand in the 7 minute timer.

    You flip the 7 minute timer back over and bingo-bango. You got 9 minutes….. this is too easy.

  13. A few notes:
    1.) I’ve been away a bit, so sorry it took me a while to mark these correct.
    2.) For the timing problem, something that wasn’t explained, and thus now might not really be a big deal is this: As I understood the question, once you start the timers, you have to be done in nine minutes, rather than taking 35 minutes to set the timers up in such a way as to guarantee minutes when next you wanted to time something. As the wording of the question doesn’t say that, I guess either type of answer will do… but most likely, people will laugh at you.
    3.) “Adan” … if that is your real name (Adam!), you need to watch Die Hard 3. or remove that crayon that’s currently lodged in your brain.

  14. Solution to #1:

    Fill (3) Bucket.
    Pour all of (3) Bucket into (5) Bucket.
    Fill (3) Bucket.
    Pour into (5) Bucket until (5) Bucket is full.
    Empty (5) Bucket.
    Pour 1 gallon remaining in (3) Bucket into (5) Bucket.
    Fill (3) Bucket.
    Pour (3) Bucket into (5) Bucket.

    1 gallon + 3 gallons = 4 gallons!!!!!

  15. Answer to #2:

    Fill (4) twice and pour into (9).
    Fill (4) and pour to fill (9).
    (3 gallons remaining in (4)).
    Empty (9).
    Pour 3 gallons in (4) into (9).
    Pour full (4) into (9)
    Fill (9).
    (2 gallons remain in (4)!).
    Empty (9)
    Pour 2 gallons in (4) into (9).
    Pour 4 gallons into (9)

    2 gallons + 4 gallons = 6 gallons!!!! omg..

  16. Solution to #3:

    Fill (5) pour until (4) is full.
    (1 gallon remaining in (5))
    Empty (4)
    Pour the 1 gallon into (4)
    Fill (5)
    Pour (5) into (4) until (4) is full.

    5 gallons – 3 gallons = 2 gallons !!!!

  17. timing problem:
    start the 7 and the 4. flip the 4 when it runs out. flip the 7 when it runs out. when the 4 runs out again flip the 7 ( 1 minute of sand will have run in the 7 ). when the 7 runs out it’ll have been 9 minutes.

  18. 1.)

    fill the 3 and empty it into the 5. fill the 3 and use it to fill the 5. you now have 1 gallon in the 3. empty the 5 and place the 1 gallon in the 5. now fill the 3 and empty it into the 5. tada you have 4 gallons.

  19. Looks like I’ll be getting a lot of laughing-at on this one. Don’t know why I’m having so much trouble understanding the indended parameters.

    Answer to the timing question as intended:
    Start both sandglasses, and flip the 4-min one when it’s done. When the 7-min finishes, flip it. When the 4-min one finishes, flip the 7-min one, which will run for one more minute, for a tottal of 9 minutes.

  20. 2.)

    fill the 4 empty into the 9. do it again so that there’s 8 in the 9. fill the 4 and use it to fill the 9 yielding 3 remaining in the 4.
    empty the 9 and place the 3 into the 9. fill the 4 and empty it into the 9. fill the 4 and use it to top off the 9 yielding 2 remaining in the 4.
    empty the 9 and place the 2 into the 9. now fill the 4 and empty into the 9.
    tada you have 6 gallons in the big bucket.

  21. 3.)

    fill the 4 and empty it into the 5. fill the 4 and use it to top off the 5.
    empty the 5 and place the remaining 3 in the 5. fill the 4 and top off the 5 yielding a remaining 2 in the 4.

  22. Solution to #4:

    Here are the buckets, each step is the outcome of each pour. I’ll be happy to elaborate if you need me to fill in the blanks.

    (7) (4) (3)

    7 0 0
    4 0 3
    4 3 0
    1 3 3
    1 4 2
    5 0 2
    5 2 0
    2 2 3

    OMG!! It’s awesome.

  23. 1. Fill the 5g bkt. Fill the 3g bkt with the 5g bkt. Empty the 3g bkt. Empty the remaining 2g from the 5g bkt into the 3g bkt. Fill the 5g bkt. Fill the 3g bkt the rest of the way with 1g from the 5g bkt, which now has 4g.

    2. Fill the 9g bkt. Fill and empty the 4g bkt twice from the 9g bkt. Empty the remaining 1g from the 9g bkt into the 4g bkt. Fill the 9g bkt. Fill the 4g bkt the rest of the way with 3g from the 9g bkt, which now has 6g.

    3. Fill the 4g bkt and empty into the 5g bkt. Fill the 4g bkt. Fill the 5g bkt the rest of the way with 1g from the 4g bkt, which now has 3g. Empty the 5g bkt. Empty the remaining 3g from the 4g bkt into the 5g bkt. Fill the 4g bkt. Fill the 5g bkt the rest of the way with 2g from the 4g bkt, which now has 2g.

    I’m not smart enough to figure out the other two.

  24. 1. 5 0
    2 3
    2 0
    0 2
    5 2
    4 1

    2. 9 0
    5 4
    5 0
    1 4
    1 0
    0 1
    9 1
    6 4

    3. 5 0
    1 4
    1 0
    0 1
    5 1
    2 4

    4. 7 0 0
    4 0 3
    4 3 0
    1 3 3
    1 4 2
    5 0 2
    5 2 0
    2 2 3

    5. 5 3 2
    4 3 3
    4 5 1

    Timing:
    1. Start Both (0 minutes) [7 4]
    2. When 4 is done, flip 4 (4 Minutes)[3 0] -> [3 4]
    3. When 7 is done flip seven (7 Minutes)[0 1] -> [7 1]
    4. When four is done, flip the 7, which now has 1 minute elapsed on it (8 minutes) [6 0] -> [1 0]
    5. When 7 is done, Time is up. (9 Minutes) [0 0]

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