I'm going to give you 10 short problems, each the same idea. You have 3 jugs of different sizes, and you want a certain amount of water in one jug only. You have to say what you'd do to get the desired amount.
Here are the rules for this experiment: You have to do all ten and you must do them in order; you can give up on any question if you can't figure it out, but take your time; and you need to identify how you did each one. Then, please put in the comments what the answer you got was, about how long the questions took you [individually or total, it doesn't matter], which question was the hardest, and which question was the easiest.
Here are the examples:
The first three numbers in each set are the jugs' capacities; the last number is the amount you want to get.Good luck, and feel free to pass this along to your friends. I want to get as many people answering this as I can; I'll post the answers and some comments later on in the day when I have a chance and after a lot of people have answered. Try not to read other people's answers and comments until after you've answered all the questions...!
- 1) 21, 127, 3 = 100
- 2) 14, 163, 25 = 99
- 3) 18, 43, 10 = 5
- 4) 9, 42, 6 = 21
- 5) 20, 59, 4 = 31
- 6) 23, 49, 3 = 20
- 7) 15, 39, 3 = 18
- 8) 28, 76, 3 = 25
- 9) 18, 48, 4 = 22
- 10) 14, 36, 8 = 6
You'll find the results fascinating - I know I did, and the two people I just tested it out on did as well. What are you waiting for?! Start!
Tags:
1 – fill up the 127 jug, then pour water out into the 21 jug, and out into the 3 jug twice
ReplyDelete2 – fill up 163 jug, pour out into 25 jug twice, then pour out into 14 jug once
3 – fill up 43, pour out into 18 once, then out into the 10 twice
4 – take two of the 6 jugs and 1 of the 9 jug and pour into the 42 jug
5 – fill up 59 jug, then pour out 20 jug once, and the 4 jug twice
6 – fill up 23 jug, then pour out 3 jug once
7 – fill up 39 jug, then pour out 15 once and 3 twice
8 – fill up 28 jug, pour out 3 jug
9 – fill up 18 jug and 4 jug and pour both into the 48 jug
10 – fill up 14 jug and pour out 8 jug
It took me about 6 minutes to do all 10 problems.
It's been pointed out to me that I didn't follow the instructions and answer all the questions, so here goes:
ReplyDeleteI started at 1, I used my math skills to do each one, the hardest was #2 (I think) and the easiest was either 9 or 10 (or 7)
Math . . . head . . . hurt . . .
ReplyDeleteAm I the only one who thought the title of this post at first was Waterbugs - Gevalt! and lifted my feet up off the floor? Yikes!
RM - You've been living in NY too long!
ReplyDeleteIt's not really math - it's quite simple, really. Try it!
1) Fill 127, spill from 127 into 21, 3, 3 = 100
ReplyDelete2) Fill 163 , spill from 163 into 14, 25, 25 = 99
3) Fill 43, spill from 43 into 18, 10, 10 = 5
4) Fill 42, spill from 42 into 9, 6, 6 = 21
5) Fill 59, spill from 59 into 20, 4, 4 = 31
6) Fill 23, spill into 3 = 20
7) Fill 15, fill 3, pour both into 39 = 18
8) Fill 28, spill into 3 = 25
9) Fill 18, fill 4, pour both into 48 = 22
10) Fill 14, spill into 8 = 6
Started from 1, 4 minutes total, 10 was hardest, 2-5 were equally easy.
I did this without looking first at the comments, and tried to rattle them off as quickly as possible. It took about 5 minutes (I didn't clock it) to answer the questions on a note pad and much longer to write this comment.
ReplyDelete1) fill 127, pour off 21, 3, 3
2) fill 163, pour off 25, 25, 14
3) fill 43, pour off 18, 10, 10
4) fill 42, pour off 6, 6, 9 (not the most efficient)
5) fill 59, pour off 20, 4, 4
6) fill 49, pour off 23, 3, 3 (not the most efficient)
7) pour from 15 and 3 into 39.
8) fill 28, pour off 3
9) pour from 18 and 4 into 48
10) fill 14, pour off 8
I set out to do them in order starting from #1, but forgot #3, which I went back to do after #4.
They were all about the same difficulty.
In real life, it would also matter what liquid units were being used (if these were large units like quarts or liters, for example, it would be easier to pour from a smaller jug than from a bigger one).
Havent tried it yet...
ReplyDeleteall I know is I've heard the answer time and again..
and have forgotten it time an again..!!
Starting at #1, here goes:
ReplyDelete#1: Fill the 127. Fill the 21 from the 127 (you're left with 106 in the 127). Fill the 3 from the 127 (now left with 103), empty the 3, and fill it again from the 127. You now have exactly 100 gallons.
#2: Fill the 163. Fill the 14 from the 163 (you're left with 149 in the 163). Fill the 25 from the 163 (now left with 124), empty the 25, and fill it again from the 163. You now have exactly 99 gallons.
#3: Fill the 43. Fill the 18 from the 43 (you're left with 25 in the 43). Fill the 10 from the 43 (now left with 15), empty the 10, and fill it again from the 43. You now have exactly 5 gallons.
#4: Fill the 42. Fill the 9 from the 42 (you're left with 33 in the 42). Fill the 6 from the 42 (now left with 27), empty the 6, and fill it again from the 42. You now have exactly 21 gallons.
#5: Fill the 59. Fill the 20 from the 59 (you're left with 39 in the 59). Fill the 4 from the 59 (now left with 35), empty the 4, and fill it again from the 59. You now have exactly 31 gallons.
#6: Fill the 23. Fill the 3 from the 23. You now have exactly 20 gallons.
#7: Fill the 15 and the 3. Pour both into the 29. You now have exactly 18 gallons.
#8: Fill the 28. Empty it into the 3. You now have exactly 25 gallons.
#9: Fill the 18 and the 4. Pour them into the 48. You now have exactly 22 gallons.
#10: Fill the 14. Fill the 8 from the 14. You now have exactly 6 gallons.
I started from #1 (obviously), and the first 6 didn't take long. I started doing the 6th and 7th in a long fashion, like I did 1-5, but then halfway through #7, I realized I was being stupid, and I then did 6-10 in the shorter, faster, easier way.
"Then, please pit in the comments..."
ReplyDeleteMind you, I do not plan on pitting my answers in the comments, thank you very much. Instead, I will haughtily and rudely nitpick on typos because I am rather cranky after another long day of school.
i hope i was correct in assuming you can pour water out of a jar into the ground. that is answer a.
ReplyDeleteif not i provide answer b.
1) 21, 127, 3 = 100
127 - (2*3) - 21 = 100.
(ie pour out into the 3, unload the 3, and pour out onto 3 again. the pour out to 21.)
2) 14, 163, 25 = 99
163 - (2*25) - 14 = 99
3) 18, 43, 10 = 5
43 - (2*10) - 18 = 5
4) 9, 42, 6 = 21
42 - (2*6) - 9 = 21
5) 20, 59, 4 = 31
59 - (2*4) - 20 = 31
6) 23, 49, 3 = 20
49 - (2 * 3) - 23 = 20
7) 15, 39, 3 = 18
15 + 3 = 18. (ie pour 15 + 3 into the 39)
8) 28, 76, 3 = 25
28 - 3 = 25
9) 18, 48, 4 = 22
18 + 4 = 22 (ie pour 18 and 4 into the 48)
10) 14, 36, 8 = 6
14 - 8 = 6
took a short amount of time, 20 or 30 seconds, once i recognized pattern it went faster.
when i got to question 7, i paused a little because the pattern didnt match, then found new pattern and again easy.
Muscat - This isn't one of those types...
ReplyDeleteEzzie... Serach put you up to this, didn't she?
ReplyDeleteThis took me about 15 minutes. I kept going back to check the rules, surprising myself that I didn't find any directing us to find the best answer, the answer that uses the least amount of water, or an answer that use all three jugs. I couldn't help but try to come up with the best answer, not only the first workable answer; that's how my brain works. I wanted to go back and re-think all my answers to optimize for efficiency, but I refrained from doing so.
ReplyDelete* 1) 21, 127, 3 = 100
Fill up 127; pour from it 21, 3, and 3.
* 2) 14, 163, 25 = 99
Fill up 25; pour from it 14, then pour the 11 remaining into 163. Repeat nine times.
* 3) 18, 43, 10 = 5
Fill up 43; pour from it 18, 10, and 10.
* 4) 9, 42, 6 = 21
Fill up 42; pour from it 9, 6, and 6.
* 5) 20, 59, 4 = 31
Fill up 59; pour from it 20, 4, and 4.
* 6) 23, 49, 3 = 20
Fill up 20; pour from it 3.
* 7) 15, 39, 3 = 18
Fill up both 15 and 3; pour both into 39.
* 8) 28, 76, 3 = 25
Fill up 28; pour from it 3.
* 9) 18, 48, 4 = 22
Fill up both 18 and 4; pour both into 48.
* 10) 14, 36, 8 = 6
Fill up 14; pour from it 8.
1) 21, 127, 3 = 100
ReplyDeleteFilll up the 127. pour into 21 once, empty 21. pour into 3 twice emptying each time.
127 - 21 - 3 -3 = 100
2) 14, 163, 25 = 99
fill up the 163, pour into 25 twice emptying each time, then pour into the 14 and empty it, 99 will be left.
Alternatively fill the 25 and pour into the 14. Empty the 14. Pour remaining 11 into 163. Repeat 9 times.
163 - 25 - 25 -14 = 99
or
9 x (25 -14) = 99 - each time you get 11, pour it into the 163
3) 18, 43, 10 = 5
Fill up the 43 pour into the 18 once and empty, then twice into the 10 emptying each time.
43 - 18 -10 - 10 = 5
4) 9, 42, 6 = 21
Fill up the 42 pour into the 9 once and empty it then into the 6 twice emptying each time.
42 - 9 - 6 - 6 = 21
5) 20, 59, 4 = 31
Fill up the 59 then pour once into the 20 emptying it and then twice into the 4 emptying each time.
59 - 20 - 4 - 4 = 31
6) 23, 49, 3 = 20
Fill up the 49 fill the 23 empty it and then pour twice into the 3 emptying each time.
Or using only two, fill up the 23 and pour into the 3, that will leave you with 20 in the 23.
49 - 23 - 3 - 3 = 20
or
23 - 3 = 20
7) 15, 39, 3 = 18
Fill up the 15 pour it into the 39, then fill up the 3 and pour it into the 39.
Or fill up the 39 and pour into the 15 and empty it then pour into the 3 twice emptying it each time.
15 + 3 = 18 (contained in the 39)
or
39 - 15 - 3 - 3 = 21
8) 28, 76, 3 = 25
I don't get this one. Fill up the 28 and then pour into the 3 and empty the three. You don't need the 76.
28 - 3 = 25
9) 18, 48, 4 = 22
Fill up the 48 pour into the 18 and empty it then pour into the 4 twice emptying it each time.
Or fill up the 18 pour it into the 48 and then fill up the 4 and pour it into the 48.
48 - 18 - 4 - 4 = 22
or
18 + 4 = 22 (contained in the 48)
10) 14, 36, 8 = 6
Fill up the 36 pour into the 14 once then empty it and then pour into the 8 twice emptying it each time.
or fill up the 14 and pour into the 6 once and empty it.
36 - 14 - 8 - 8 = 6
or
14 - 8 = 6
It took me about 10 minutes.
Nu, Ezzie, are you going to come back and tell us what the conclusions of this here experiment are? Is it that we might continue following the pattern and filling the largest jug then pouring off into the smaller ones even when it is easier to fill the smaller ones and empty them into the larger one? I know that, though I could have done that for the fourth example, I didn't get trapped in that pattern for the duration, nor did most others.
ReplyDeleteI actually really like these types of brain teasers, except this batch was too straightforward and easy. But I understand your reason for presenting them to us was not about solving the puzzles themselves.
I like the ones that are more difficult, with bi-directionality of pouring and with techniques not used in any of these examples. An elementary example of the type I like might be using a 7-unit and 3-unit jug to end up with 5 units of water.
I also like the coin-weighing puzzles; have you ever done those?
Soon... :)
ReplyDelete