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Riddles with weighings and transfusions
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Riddles in Russian | Riddles in Ukrainian
Riddles with weighing and transfusions in Russian The winemaker usually sells his wine in 3 and 5 liter sizes and only uses jars of this size for this. One of the buyers wanted to buy 1 liter. How did the winemaker measure out 1 liter to him using his own pitchers?
(First, he filled the 3-liter jug and poured its contents into the 5-liter jug. Then he filled the 3-liter jug again and topped up the 5-liter jug from it until it was full. As a result, he had 1 liter left in the jug)
There are 13 coins, of which only one is fake, and it is not known whether it is lighter than real or heavier. You need to find this coin in three weighings. Scales - standard for tasks of this type: two cups without weights.
(Let's put aside the thirteenth coin, and denote the others in this way: FAKE MIND CLOT. Now weigh one quadruple against another (the letters mark the coins that are included in each quadruple): MA DO - LIKE, ME TO - FIND, FAKE - COIN. Now it's quite easy to find a counterfeit coin if it is included in these twelve coins.For example, if the results of the weighing were: lighter to the left, equals, lighter to the left, then only coin "A" can be counterfeit, which is lighter than the others. the thirteenth coin we set aside? Everything is very simple: in this case, with all three weighings, the scales will be balanced)
There are 9 coins. There are only scales. Scales are ordinary, laboratory (cup). One of the 9 coins is lighter than all the others. How to determine which coin is lighter? Coins on the scales can be weighed only 2 times.
(Let's divide 9 coins into 3 coins in a pile. We put two of the 3 piles on different sides of the scales. If the scales are not outweighed to one of the sides, then it turns out that the weight of the coins is even, therefore, the light coin remained in the unweighted 3rd pile. With 3 coins left, we do the same. We weigh two coins. If their weight turned out to be even, then the unweighted coin will be light)
3 Maharajas with their three peris approached the bank of the Ganges River, intending to cross to the other side. But local customs did not allow any peri to remain in a boat or on the shore with someone else's Maharaja, if there was no one nearby. There was only one boat on the shore, designed for 2 people. Fortunately, customs did not forbid any of the peris to drive the boat herself. How, under such conditions, can everyone cross to the opposite shore?
(Let's replace the Maharajas with the letters A, B, C, and peri a, b, c. An empty place in a boat or on the shore is indicated by a dot (.). Then, schematically, the crossing will look like this:
Left bank Right bank
A B C ...
a B C ...
1. Two peris are sent first:
A B C ...
a . . . b c
2. One of the peris returns by itself and carries the third peri:
A B C . . . . . a B C
3. One peri returns and stays with her maharaja, and the other two maharajas go to the right bank:
BUT . . . B C
a . . . b c
4. One maharaja with his peri returns to the left bank, and the peri remains there, and two maharajas go to the right bank:
. . . A B C
a b . . . in
5. Now the peri moves and takes the other peri with him:
. . . A B C
a . . . b c
6. Behind the last peri goes her maharajah or another peri:
. . . A B C
. . . a B C
And that's all on the right bank - and no one drowned, and not a single custom was violated)
There are ten numbered hats on the table. Each hat contains ten gold coins. One of the hats contains counterfeit coins. A real coin weighs 10 grams, and a fake one only 9. A scale with a scale in grams is given to help. How to determine which of the hats contains counterfeit coins, using the scales for only one weighing? Scales can weigh no more than 750 grams.
(We take one coin from the first hat, two from the second, three from the third and so on, put all these coins on the scales.
If all coins were real, then the weight would be: 10*(1+2+3+4+5+6+7+8+9+10). Together: 550 grams. But a few coins are counterfeit, and how many are easy to find out. It is enough to take away the weight that we received from 550, and we will see an "error" equal to the number of counterfeit coins. The number of coins will indicate the hat)
In front of you is a jug that contains 4 liters of wine. You need to divide these 4 liters equally between two comrades, but you only have two empty jugs from the dishes: one that holds 2,5 liters and the other that holds 1,5 liters. How to divide 4 liters of wine into two using only these three vessels?
(From a 4-liter jug we fill 2,5 liters, then, from 2,5 liters we fill 1,5 liters. As a result, in a 4-liter jug - 1,5 liters, in a 2,5-liter - 1 liter and in 1,5 liter - 1,5 liters Next: pour the contents of a 1,5 liter jug into a 4 liter jug, and the contents of a 2,5 liter jug into a 1,5 liter jug. We get: in a 4 liter jug - 3 liters , in a 2,5 liter jug - 0, and in a 1,5 liter jug - 1 liter Now from a 4 liter jug we fill a 2,5 liter jug, and then from a 2,5 liter jug we add 1,5 liter, 0,5 liters We get 2,5 liters in a 2 liter jug, pour the contents of a 1,5 liter jug into a 4 liter jug and get 2 liters in it. As a result, in a 4 liter jug and in a 2,5 liter jug, 2 liters guilt)
Tanya is standing on the bank of the river. She has two earthenware jars: one is 5 liters, and Tanya remembers only about the second that it holds either 3 or 4 liters. Help Tanya determine the capacity of the second jug. (Looking into the jug, you can not understand how much water is in it.).
(1. We fill a 5 liter jug with water. Pour it into the second jug. In the 5 liter jug there will be either 2 liters if the second jug is 3 liter, or 1 liter if the second jug is 4 liter.
2. Pour water from the second jug back into the river. And the contents of the fifth 5 liter jug are again poured into the second jug.
3. We collect water in a five-liter jug and pour water from it into the second. As a result, 5 liters will remain in the 4 liter jug if the second jug is 3 liter, or 2 liters if the second jug is 4 liter.
4. Pour out the water from the second jug. Pour the contents of the 5 liter jug into the second jug. If all the water does not fit in the second jug - it is 3 liters, otherwise it is 4 liters)
Riddles with weighing and transfusions in Ukrainian
Vinorob zazvichay sell your wine for 3 and 5 liters and vikoristovu for that glider only this size. One of the buyers wants to buy 1 liter. How is a wine grower seeing yoma 1 liter crusty with wet gleams?
Vidpovid
(A bunch of wines filled with a 3-liter glacier and poured into a 5-liter yogo. Then we refilled with a 3-liter glacier and topped up from a new to full filling with a 5-liter glacier. As a result, 1 liter was filled in the glacier)
3 maharajas from three yards came to the bank of the river Ganges, trying to cross to the other bank. Ale mіstsevі zvichaї did not allow the yearly feather to be left in the chovnі, or on the birch tree from someone else's maharaja, as if the entrustment would not be his own. On the birch, there was less than one choven, repayments for 2 people. Fortunately, the zvichas did not hinder the future of their own reign. How, for such minds, can we move to the opposite coast?
Vidpovid
(Replacing the Maharaja with the letters A, B, C, a, a, b, c. An empty space on a birch is indicated by a dot (.). Then, schematically, the crossing will look like this:
Libyan coast Right coast
A B C ...
a B C ...
1. Two feathers are adjusted to the back:
A B C ...
a . . . b c
2. One perimeter rotates itself and transports the third perimeter:
A B C . . . . . a B C
3. One lane turns around and is deprived of its maharaja, and two other maharajas head to the right bank:
BUT . . . B C
a . . . b c
4. One Maharaja with his lanes turns to the left bank, and the lanes are left there, and two Maharajas head to the right bank:
. . . A B C
a b . . . in
5. Now you are going to take the next pen with you:
. . . A B C
a . . . b c
6. For the rest of the month, the Maharaja or the other month:
. . . A B C
. . . a B C
І from the mustache on the right bank - and without drowning, and zhoden sound no damage)
Є 13 coins, only one of them is false, moreover, it is unknown, it is easier than the right one or more important. It is necessary to know the qiu coin for three zvazhuvannya. Terezi - standard for the head of the type: two cups without weights.
Vidpovid
(It is possible to kill thirteenth coin, and otherwise it is significant in this way: FAKE MIND CLOT. Now we count one four against another (the letters mean the coins that enter the skin four): MA DO - LIKE, ME TO - FIND, FAKE - COIN. Now we just need to know the counterfeit coin, as if there were twelve coins in it. yu show up all- did we deposit thirteen coins?
Є 9 coins. Only one vag. Terezi zvichayny, laboratory (cups). One of 9 coins is lighter, lower is all else. How to designate a coin as a light one? Coins on vaga can only be called 2 times.
Vidpovid
(We will distribute 9 coins of 3 coins from the merchant. Two of 3 kopecks will be put on different sides of the teres. If the teres were not transported to one side, then it turns out that a bunch of coins є equal, well, a light coin was lost in the unimportant 3rd merchants. With 3 coins, which are lost, it’s worth it. Two coins are important. If your vaga appeared even, then the coin will be light and unimportant)
There are ten numbered capelyukhs on the table. At the skin drop lie ten gold coins. In one of the droplets there are counterfeit coins. The right coin is worth 10 grams, and only 9 grams are added. How can one signify in a capelyuhіv false coins, vicarious vagaries only for one zvazhuvannya? Wags can weigh no more than 750 grams.
Vidpovid
(From the first drop we take one coin, from the other two, from the third three, etc., we put all the coins on the vag.
Yakbi all coins were correct, then vaga bula b: 10 * (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10). Together: 550 grams. Ale kіlka coins are fake, and skilki are easy to get. To finish from 550 vіdnyati that vаgu, scho we have gained and we are more likely to "fault", equal to the number of counterfeit coins. The number of coins is about a drop)
In front of you is a glechik, which will take 4 liters of wine. You need to share 4 liters between two comrades, but you have only two empty glaciers for dishes: one that holds 2,5 liters, the other that holds 1,5 liters. How to pour 4 liters of wine for two for the help of only three vessels?
Vidpovid
(For a 4-liter glacier, we fill in 2,5 liters, then, for a 2,5-liter one, we fill in 1,5 liters. As a result, in a 4-liter - 1,5 liters, in a 2,5-liter - 1 liter and 1,5 liter - 1,5 liters. , in 1,5 liter - 4, and in 2,5 liter - 1,5 liter Now from 4 liter glacier we will add 3 liter glacier, and then from 2,5 liter glacier we will add 0 liter, 1,5 liter. 1 liters guilt)
Tanya is standing on the birch of the river. She has two clay gliders: one - for 5 liters, and about the other Tanya remembers only those who drink wine, sometimes 3, sometimes 4 liters. Help Tanya to designate the capacity of another fleck. (Looking into the glechik, you can’t understand, skilki in a new water.).
Vidpovid
(1. We collect water in a 5 liter glacier. We pour it into another chalice. In a 5 liter chalice, either 2 liters will be left, if another glacier is 3 liter, or 1 liter, if another 4 liter glacier.
2. We pour water from another little chalet back to the river. And instead of the fifth 5 liter gleck, I will again pour it into another jelly.
3. We collect water in a five-liter calf and pour the new water into another. As a result, a 5 liter glacier will lose 4 liters, like another 3 liter glider, or 2 liters, like another 4 liter glimmer.
4. We pour water from another little chalet. It is poured into a 5 liter glacier into another chalice. If all the water does not fit into another glech - wine is 3 liters, and otherwise - 4 liters)
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