Two Jars
by Serhiy Grabarchuk, Jr.
Home / Puzzle Playground / Puzzles / Math 'n' Logic /
6L
9
6L
4
Two jars made of very fine glass are shown in the illustration. They both have the
same capacity–6L. Each jar is of the round profile, but since they are also of the
same capacity, the left jar with the smaller profile is higher – 9 units, while the
right jar with the bigger profile is lower–only 4 units high.
Having an immense supply of water the object is to measure 4L of water with the
help of these jars.
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Last Updated: December 7, 2007
Puzzle concept: Copyright © 2007 by Serhiy Grabarchuk, Jr.
Web page: Copyright © 2007 ThinkFun Inc. All Rights Reserved.
Permission is granted for personal use only.
This puzzle may not be duplicated for personal profit.
Page 1 of 3
Two Jars
Solution
Home / Puzzle Playground / Puzzles / Math 'n' Logic /
36 cubic units = 6L
36
36
cubic
units
cubic
units
6L
9
4
6L
4
9
square
units
square
units
2
Both jars are the circular cylinders. The volume of a circular cylinder is πr h, where r is the radius of the
bases, and h is the perpendicular distance between the planes that contain the bases. In our case h is
the height of a jar. Since the volume of each jar is identical, but their heights are different, then,
obviously the radii of their respective bases are also different. Thus, the bases' areas of each jar are:
higher jar: πr2 = 6/9.
lower jar: πr2 = 6/4.
Let's multiply both decimals by 6:
higher jar: 6/9 x 6 = 36/9 = 4 (the area of the higher jar's base in square units).
lower jar: 6/4 x 6 = 36/4 = 9 (the area of the lower jar's base in square units).
Since we've multiplied both decimals by 6 we can describe the volumes of the jars as 36 cubic units
each. That means 1 liter equals 6 cubic units. In order to measure 4 liters we have to get 24 cubic units
of water in one of the jars.
Last Updated: December 7, 2007
Puzzle concept: Copyright © 2007 by Serhiy Grabarchuk, Jr.
Web page: Copyright © 2007 ThinkFun Inc. All Rights Reserved.
Permission is granted for personal use only.
This puzzle may not be duplicated for personal profit.
Page 2 of 3
Two Jars
Solution
Home / Puzzle Playground / Puzzles / Math 'n' Logic /
36
cubic
units
36
cubic
units
Step 1. Fill out both jars - 36 cubis units of water in each.
36
cubic
units
16
cubic
units
20
cubic
units
Step 1
Step 2
36
cubic
units
20
cubic
units
Step 3
36
20
cubic
units
cubic
units
20
20
20
16
cubic
units
Step 3. Get the higher jar out of the lower one.
Step 4. Pour the water from the higher jar into the lower
one until the latter is brimful again. Since the lower jar
contains 20 cubic units of water already, the 16 cubic
units will be poured into it from the higher jar. Now there
are 20 cubic units of water in the higher jar and 36 - in
the lower.
Step 4
cubic
units
Step 2. Place the higher jar into the lower. Such a
procedure will displace a certain volume of water from
the lower jar. Ignoring the thikness of the jar's glass, the
volume left in the lower jar will be equal the product of
the jar's height (i.e. 4) and the difference between the
areas of both jars' bases (i.e. 9-4). In other words the
volume of water left in the lower jar equals 4 x (9-4) = 4 x
5 = 20 cubic units.
cubic
units
cubic
units
Step 5. Place the higher jar once again into the lower
one. The procedure like in the step 2 will leave in the
lower jar 20 cubic units, displacing 16 cubic units of
water.
20
cubic
units
Step 5
Step 6
36
4
cubic
units
Step 6. Get the higher jar out of the lower one.
cubic
units
Step 7. Pour the water from the higher jar into the lower
one until the latter is brimful again. Like in step 4 this will
add 16 cubic units to the lower jar and thus, 4 cubic units
are left now in the higher jar.
4
cubic
units
16
cubic
units
20
cubic
units
Step 7
4
cubic
units
Step 9
Step 8
20
cubic
units
0
cubic
units
24
cubic
units
Step 8. Place the higher jar once again into the lower
one. The procedure like in the steps 2 and 5 will leave in
the lower jar 20 cubic units, displacing 16 cubic units of
water from it.
Step 9. Once again get the higher jar out of the lower
one. Now the total volume of the water in both jars is 24
cubic units - 4 in the higher and 20 in the lower one.
Step 10. Pour all the water either from the higher one
into the lower or vice versa - from the lower into the
higher. Now one of the jars holds the volume of the
water which has been sought for, i.e. 24 cubic units or 4
liters.
Step 10
Last Updated: December 7, 2007
Puzzle concept: Copyright © 2007 by Serhiy Grabarchuk, Jr.
Web page: Copyright © 2007 ThinkFun Inc. All Rights Reserved.
Permission is granted for personal use only.
This puzzle may not be duplicated for personal profit.
Page 3 of 3