School-Safe Puzzle Games

Math Puzzle- The 2 Buckets

bucket ball math puzzle

We have two buckets of the same size. The first one has 1 ball inside and the second has two balls inside.
Every 3 seconds,  each ball in both buckets doubles itself. The first bucket takes 5 minutes to fill. How much time will the second one need?

Thanks to Tsopi for contributing!

Answers can be entered in the comment section below; will unmask Wednesday

34 Comments to “Math Puzzle- The 2 Buckets”

  1. Obiwan | Profile

    At any point in time the volume of bucket two will be twice that of one. Therefore, two will be 3 seconds ahead of 1 (or 4 minutes and 57 seconds).

  2. Falwan | Profile

    It take the 2 ball bucket almost 1 MINUTE to be full!

  3. Hex | PUZZLE MASTER | Profile

    After 3 seconds, the 1st bucket will have 2 balls inside, ie the same as the 2nd bucket.
    Hence the second bucket will take 5 minutes less 3 seconds or 4 minutes 57 seconds to fill up.

    Contrary to quick perception, it is not half of 5 minutes.

  4. engjs1960 | Profile

    Four minutes.

  5. engjs1960 | Profile

    Sorry, misread the question. 4 minutes 57 seconds.

  6. suineg | PUZZLE MASTER | Profile

    The first bucket takes 5 min to fill and has 1 ball in it
    The second bucket has 2 balls in it.. the first bucket is equal to the second bucket 3 seconds after so .. the second bucket takes 3 second less than the first bucket to fill so 4 minutes and 57 seconds right.
    Final answer 4 min 57 seconds, cool

  7. Shawn | PUZZLE GRANDMASTER | Profile

    What doubles? The diameter? The circumference? The volume?

    If the volume doubles every 3 seconds, then the second bucket would take 4min57sec to become full.

  8. munna | Profile

    4 minutes 57 seconds

  9. Ari | Profile

    The second bucket is one step ahead of the first bucket, thus 3 seconds ahead.
    So logically the second bucket fills 3 seconds before the first in 4:57.

  10. infinityaurora314 | Profile

    4 minutes and 57 seconds? You didn’t say the balls were the same size, though.

  11. mrman | Profile

    4 minutes and 57 seconds.

  12. BlindCupid | Profile

    It would need 4 minutes 57 seconds to fill.

    The bucket with one ball first doubles its balls ending up with two, and it keeps on doubing until it reaches 5 minutes

    The bucket with two balls started with two balls, which is the same as the bucket 1’s balls after it has doubled once.

    Therefore the difference between the two buckets is only one double. Bucket one doubled is bucket two’s balls. 1 doubled is two.

    It takes 3 seconds for it to double once.

    Since the first bucket needed five minutes to double,
    five minutes – 3 seconds = four minutes and 57 seconds.

    The second one would need 4 minutes 57 seconds to fill.

  13. jamesbuc | Profile

    4 minutes 57 seconds

  14. Blusummers13 | Profile

    Assuming the balls are the same size in both buckets and assuming that the doubled balls also double (1, 2, 4, 8…;) then bucket 2 will be full 3 seconds before bucket 1.

    4 minutes and 57 seconds to full.

  15. brianu | Profile

    4 minutes and 57 seconds

  16. Yar | Profile

    Started to do all the math, but halfway through it realized that bucket 2 is simply one step ahead of bucket 1. In other words, bucket 2 is always just 3 seconds ahead of bucket 1. So, 4 minutes and 57 seconds.

  17. Tsopi | Profile

    Pretty amazed all you guys found it…it took years for my friends to make this thought!!!

  18. satpal_sharma | Profile

    if First Bucket takes 5 minutes to fill. then second will take 4.57 minutes to fill.

  19. Hendy | Profile

    There are some very important questions to ask for this problem:

    1) What part of the balls is doubled? Is it the volume of each ball, the surface area of each ball, the radius of each ball, is it the number of balls, or is there some other form of doubling that I have not guessed correctly? The problem statement is not clear on this point. The answers to this set of questions impacts the remaining questions most of which would be of consequence if “number of balls” is not the answer.

    2) What constitutes “full”? A ball reaching the mouth of the bucket? Assuming that the ball could have its contents emptied into the bucket–must the balls have exactly the same volume as the bucket? Does full constitute the balls pressing on the side of the bucket, no longer able to expand without breaking the bucket. A related question: are the balls rigid, flexible, collapsible/compressible, fluid, gaseous, or in someway variable in size and shape?

    3) If the size of the balls are changing (see question set 1), I would have to assume that the volume of a sphere (and therefore the radius of each ball) is related to the answer.

    4) Does this problem assume absolute settling of the balls? This would have to assume a perfect, friction-free environment (balls perfectly smooth, bucket perfectly smooth, and a perfect vacuum within the bucket). It would also assume that gravity or some other force has a part in this. If it is in a gravity-free environment, then any forces placed on the balls would impact whether the bucket becomes/stays full. If the balls could have settling issues, there is a potential for randomness that could cause filling to be premature (back to the question of what constitues “full”;) for one or the other buckets.

    5) Are we assuming someone has a supply of balls that will fill up the bucket and can effectively double the number of balls by adding twice as many balls each three seconds? On the other hand are we assuming intantaneous, spontaneous generation? Is this a theory in theory or are we doing something practical here?

    I work as a Contractor to Government programs and as an engineer. Can you tell? We have to be very specific and careful for what problem statements are given to us and how we design things. It is very easy to end up with a $1M bucket and set of balls if we aren’t careful.


  20. Shawn | PUZZLE GRANDMASTER | Profile

    “It is very easy to end up with a $1M bucket and set of balls if we aren’t careful.”

    Given the ridiculously inflated prices that we have heard about government paying for various items, it appears that many contractors’ set of balls have doubled many times over!

    This problem requires adherence of agreed-upon definitions of “full” and “double” which are based on daily experience; if not stated, the parameters are assumed to be the standards that we as a society have come to accept. Hendy, I imagine that your specialized skill-sets would require that you continually “change gears” to match the background of your various conversation partners. I am reasonably certain, however, that Tsopi is not a government agent in charge of obtaining bids for a bucket-filling contract!

  21. RK | Founder | Profile

    “Given the ridiculously inflated prices that we have heard about government paying for various items, it appears that many contractors’ set of balls have doubled many times over!”

    HA! That had me laughing my @#%$* off!
    (need to get some better animated emoticons)

  22. Shawn | PUZZLE GRANDMASTER | Profile

    This emoticon is just a drop in the bucket…

  23. Hex | PUZZLE MASTER | Profile

    Tsopi must confirm or deny his alleged status as a government agent in charge of obtaining bids for a bucket-filling contract, and whose set of balls have doubled many times over :D

    And all of this was deduced from the 2 buckets puzzle :agape

  24. alyson | Profile

    4 min 57 seconds

  25. Harpreet | Profile

    Two hours and thirty minutes.

  26. deepside0058 | Profile

    4 minutes and 57 seconds.
    so easy!!!

  27. M.Pink | Profile

    1) In the first bucket, 5 minutes is required to fill the bucket, if each 3 second the number of the ball doubles, which means the total ball at the end of 5 minutes will be 200.
    2) Since the second bucket has 2 balls initially, which means, it needs 100 times (x100) to reach the maximum number of balls. Since each 3 sec is double, so 100/2, So it needs to double 50 times to obtain 200 balls.
    3) Since each double is 3 sec, 50 times will be 50 x 3 = 150 second. The total time for it to fill will be 2 min and 30 sec.

  28. atulatul | Profile

    2 min 30 sec

  29. Sarah Al Taher | Profile

    easy quiz…5 min = 5*60 sec=300sec>>>300/3=100 time of doubling>> we multiply the first number of balls by 2(100) (2 to the power 100)so 1*2(100) = 2(100)balls in a filled bucket
    but the second bucket contains 2 balls so :
    2 * 2(number of doubling times)=2(100)
    2(number of doubling times + 1 )=2(100)
    >>>>number of doubling times = 100 – 1 = 99 time== 99*3sec = 297 sec = 4 min 57 sec :))) or simply can say 100-1 times === 5 min – 3 sec :)))

  30. Kryptik | Profile

    This puzzle really got me thinking!

  31. Tsopi | Profile

    Well i don’t know how to re-edit the puzzle but to answer to some of you:
    What i say doubles itself i mean that it copies it self.Genarating another one identical.It is like every 3 seconds we look how many balls we the bucket has x balls we put another more x and now the bucket has x+x = 2x balls

  32. RogHyde | Profile

    They must be very large buckets or very small balls (or maybe grains of sand)!
    In 5 minutes the first ball would double 100 times (5 x 60 seconds divided by 3).
    Which I think comes to 1,267,650,600,228,230,000,000,000,000,000 balls (or thereabouts).
    Regardless of the numbers, the second bucket, starting with two balls will reach that number in three seconds less than the first bucket because that is the time it took the first ball to double itself- or 4 minutes 57 seconds.

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