There are scales without weights and 3 identical in appearance coins, one of which is fake: it is lighter than the real ones (the real coins are of the same weight). How many weightings are needed to determine the counterfeit coin? Solve the same problem in the cases where there are 4 coins and 9 coins.
We have scales without weights and 3 identical in appearance coins. One of the coins is fake, and it is not known whether it is lighter or heavier than the real coins (note that all real coins are of the same weight). How many weighings are needed to determine the counterfeit coin? Solve the same problem in the cases where there are 4 coins and 9 coins.
On a table five coins are placed in a row: the middle coin shows heads and the rest show tails. It is allowed to turn over three adjacent coins simultaneously. Is it possible to get all five coins to show heads after turning the coins over several times?
48 blacksmiths must shoe 60 horses. Each blacksmith spends 5 minutes on one horseshoe. What is the shortest time they should spend on the work? (Note that a horse can not stand on two legs.)
There are 6 locked suitcases and 6 keys for them. It is not known which keys are for which suitcase. What is the smallest number of attempts do you need in order to open all the suitcases? How many attempts would you need if there are 10 suitcases and keys instead of 6?
Jack the goldminer extracted 9 kg of golden sand. Will he be able to measure 2 kg of sand in three goes with the help of scales: a) with two weights of 200 g and 50 g; b) with one weight of 200 g?
In one move, it is permitted to either double a number or to erase its last digit. Is it possible to get the number 14 from the number 458 in a few moves?
From a set of weights with masses 1, 2, ..., 101 g, a weight of 19 grams was lost. Can the remaining 100 weights be divided into two piles of 50 weights each in such a way that the masses of both piles are the same?
Jack and Ben had a bicycle on which they went to a neighborhood village. They rode it in turns, but whenever one rode, the other walked and did not run. They managed to arrive in the village at the same time and almost twice as fast than if they had both walked. How did they do it?
Three tourists must move from one bank of the river to another. At their disposal is an old boat, which can withstand a load of only 100 kg. The weight of one of the tourists is 45 kg, the second – 50 kg, the third – 80 kg. How should they act to move to the other side?