Measuring out 10 quarts

[DivineNathicana]

Yeah, it works out perfectly. Thank you, C1ay! By the way, is there any pattern or something? I see that the 7-quart cup goes in a pattern of 7,7,0,7,1,1,0,7,0,7,2,2,0,7,0,7,3,3, etc. Why doesn't the firts part fit in? And why exactly do we arise at this pattern? Like, the 10 will obviously be in the 13 quart cup because the 7 can't fit it and it's harder to take away 9 than three... And so we know we have to take three away, which we do, a we see by the pattern, but how exactly does that happen?

 

- Alisa

[Kent]

What's to elaborate on? THe left column is the 19 quart container, the middle is the 13 and the right column is the 7. Start by pouring the 13 quart into the 19. Next pour the 7 into the 13. Next pout 7 of the 13 from the 19 quart container into the 7 quart container. Next fill the 13 from the 7 leaving 1 in the 7, etc. Each step shows only 1 pour.

 

 

hmm...then i must of misunderstood the problem

[C1ay]

Yeah, it works out perfectly. Thank you, C1ay! By the way, is there any pattern or something? I see that the 7-quart cup goes in a pattern of 7,7,0,7,1,1,0,7,0,7,2,2,0,7,0,7,3,3, etc. Why doesn't the firts part fit in? And why exactly do we arise at this pattern? Like, the 10 will obviously be in the 13 quart cup because the 7 can't fit it and it's harder to take away 9 than three... And so we know we have to take three away, which we do, a we see by the pattern, but how exactly does that happen?

 

- Alisa

 

There is a pattern but it's not evident from looking at one column by itself. If you use some type of symbolic notation to represent the 3 containers and an operator to show which is poured into which you should spot a repeating sequence. Try labeling the 3 containers something like A, B and C. Use an > to represent a pour. Then you can right an equation for each line like B > A for the first pour and C > B for the second, etc. Look for a pattern in the equations.

[DivineNathicana]

I don't know... I'm not really getting anything coherent. Or maybe it's the lack of sleep... I've been staring at a whole bunch of these problems for a while now, and I can't seem to make sense of this particular one, even with the order all right. An explanation is asked for. A thought pattern. Sadly, mine is currently "blaaaaa......" and I don't think that will suffice. = /

 

I mean like, logically, if one is to think about how to obtain 10 quarts, what would he come up with? What must be done? Three quarts must be taken away, but how? Blah.

[C1ay]

I don't know... I'm not really getting anything coherent. Or maybe it's the lack of sleep... I've been staring at a whole bunch of these problems for a while now, and I can't seem to make sense of this particular one, even with the order all right. An explanation is asked for. A thought pattern. Sadly, mine is currently "blaaaaa......" and I don't think that will suffice. = /

 

I mean like, logically, if one is to think about how to obtain 10 quarts, what would he come up with? What must be done? Three quarts must be taken away, but how? Blah.

 

Look at it this way. The sequence is extended a few steps to make the pattern more obvious. The repeating pattern starts after the 4th pour. The arrows point in the direction of the pour.

 

0	13	7	=	A	B	C
13	0	7	=	A	<	B
13	7	0	=	B	<	C
6	7	7	=	A	>	C
6	13	1	=	B	<	C
19	0	1	=	A	<	B
19	1	0	=	B	<	C
12	1	7	=	A	>	C
12	8	0	=	B	<	C
5	8	7	=	A	>	C
5	13	2	=	B	<	C
18	0	2	=	A	<	B
18	2	0	=	B	<	C
11	2	7	=	A	>	C
11	9	0	=	B	<	C
4	9	7	=	A	>	C
4	13	3	=	B	<	C
17	0	3	=	A	<	B
17	3	0	=	B	<	C
10	3	7	=	A	>	C
10	10	0	=	B	<	C
3	10	7	=	A	>	C
3	13	4	=	B	<	C