Water and Weighing Puzzles
Pouring water I.
If you had a 5-litre and a 3-litre bowl and access to water. How would you measure exactly 4 litres?
Pouring water II.
Having three bowls: 8, 5 and 3 litres capacity. Share 8 litres in halves (4 + 4 litres) pouring water the minimum times.
Pouring water III.
Having three bowls: 7, 4 and 3 litres capacity. Only the 7-litre is full. Pouring the fewest times gain the quantity of 2, 2 and 3 litres.
Pouring water IV.
How can you measure 6 litres of water using only 4 and 9-litre bowls.
Pouring water V.
Measure exactly 2 litres of water if you have:
1. 4 and 5-litre bowls
2. 4 and 3-litre bowls
Pouring water VI.
Imagine having three bowls. In the bowl A (8 litres capacity) are 5 litres of water. In the bowl B (5 litres capacity) are 3 litres of water. In the bowl C (3 litres capacity) are 2 litres of water.
Can you measure exactly 1 litre, pouring only 2 times?
Weighing I.
Imagine you have 10 bags full of coins, in each bag 1000 coins. In one bag, there are all coins forgeries. The original coin is 1 gram light, forgery is 1.1 gram.
Balancing just once on an accurate weighing-machine, how can you identify the bag with forgeries? And what if you didn't know how many bags contain forgeries?
Weighing II.
Real gummy drop bears have a mass of 10 grams, while imitation gummy drop bears have a mass of 9 grams. Spike has 7 cartons of gummy drop bears, 4 of which contain real gummy drop bears, the others imitation.
Using a scale only once and the minimum number of gummy drop bears, how can Spike determine which cartons contain real gummy drop bears?
Weighing III.
This puzzle is a step further than the previous one (weight of fake and non fake coins is the same as the weight of bears in the previous puzzle). You have eight bags, each of them containing 48 coins. Five of these bags contain only true coins, the rest of them contain fake coins. Fake coins weigh 1 gram less than the real coins. You do not know what bags have fake coins and what bags have real coins. You can use a scale, a dynamometer type one, with precision up to 1 gram (an accurate weighing machine).
Weighing only once and using the minimum number of coins, how can you find the bags containing the fake coins?
Weighing IV.
One of twelve pool balls is a bit lighter or heavier (you do not know) than the others. At least how many times do you have to use an old pair of scales to identify this ball?
(a pair of scales = a scale consisting of a lever resting on a fulcrum with weighing pans at each end of the lever equidistant from the fulcrum)
Weighing V.
On a Christmas tree there were two blue, two red and two white balls. All seemed the same, however in each colour pair one ball was heavier. All three lighter balls were the same weight, just like all three heavier balls.
Using a pair of scales twice, identify the lighter balls.
Weighing VI.
Having 9 balls, equally big, equally heavy. Only one of them is a bit heavier.
How would you identify it if you could use a pair of scales only twice?
Weighing VII.
Having 27 table tennis balls, one is heavier than the others.
What is the minimum number of weighings (using a pair of scales) needed to guarantee a confirmation of which ball is the heavy one? Of course, the other 26 balls weigh the same.
Weighing VIII.
Suppose that the objects to be weighed may range from 1 to 121 pounds at 1-pound intervals: 1, 2, 3,..., 119, 120, 121. After placing one such weight on either of two weighing pans of a pair of scales, one or more precalibrated weights are then placed in either or both pans until a balance is achieved, thus determining the weight of the object.
If the relative positions of the lever, fulcrum, and pans may not be changed, and if one may not add to the initial set of precalibrated weights, what is the minimum number of such weights that would be sufficient to bring into balance any of the 121 possible objects?
Sand-glass I.
Having 2 sand-glasses: one 7-minute and the second one 4-minute. How can you correctly time 9 minutes.
Sand-glass II.
A teacher of mathematics used an unconventional method to measure time for a test lasting 15 minutes. He used just a sand-glass, which spills in 7 minutes and a second sand-glass, which spills in 11 minutes. During the whole time he turned sand-glasses only 3 times. Explain how the teacher measured 15 minutes.
Igniter Cords
Your job is to measure 45 minutes, if you have only two igniter cords and matches to light the cords. The two igniter cords have the following features:
- They are twisted from various materials and also different parts can burn at different speed (e. g. after ten minutes they will not burn at the same point).
- Every cord burns from ignition to the end exactly one hour.
Describe your way of measuring the 45 minutes.
