Problems

A snail climbs a 10-meter high tree. In day time the snail manages to climb 4 meters, but slips down 3 meters during the night time. How long would it take the snail to reach the top of the tree if it started the journey on a Monday morning?

A candle that burns out completely in one hour costs \(60\) pence and a candle that lasts for \(11\) minutes costs \(11\) pence. For some reasons which he doesn’t want to explain to the seller, Mr. Fawkes wants to measure exactly \(1\) minute with some of these candles. Can he manage to do that if he has only \(1\) pound and \(50\) pence to spend on the candles?
Mr. Fawkes can only measure the whole interval with each of the candles. He is not guaranteed that any of the candles burns uniformly, so he cannot divide it into two parts. He cannot make it burn faster by igniting them from both ends, but he can extinguish a candle and light it up again later.

Multiplication of numbers. Restore the following example of the multiplication of natural numbers if it is known that the sum of the digits of both factors is the same.

Restore the example of the multiplication.

There is a 12 litre barrel filled with water, and two empty barrels (one is 5 litres in volume and the other is 8 litres). Using these barrels, try to

a) divide the water into 2 parts with volumes: 3 litres and 9 litres;

b) divide the water into 2 parts with equal volume.

There are 6 locked suitcases and 6 keys to them. At the same time, it is not known to which suitcase each key fits. What is the smallest number of attempts you need to make in order to open all the suitcases for sure? And how many attempts will it take there are not 6 but 10 keys and suitcases?

Decipher the following rebus (see the figure). Despite the fact that only two figures are known here, and all others are replaced by asterisks, the example can be restored.

Three people A, B, C counted a bunch of balls of four colors (see table).

Each of them correctly distinguished some two colors, and confused the numbers of the other two colours: one mixed up the red and orange, another – orange and yellow, and the third – yellow and green. The results of their calculations are given in the table.

How many balls of each colour actually were there?

A family went to the bridge at night. The dad can cross over it in 1 minute, the mom can cross it in 2, the child takes 5 minutes, and grandmother in 10 minutes. They have one flashlight. The bridge can only withstands two people at a time. How can they all cross the bridge in 17 minutes? (If two people pass, then they go at the lower of their speeds.) You can not move along a bridge without a flashlight. You can not shine it from a distance.

In Mexico, environmentalists have succeeded in enacting a law whereby every car should not be driven at least one day a week (the owner informs the police about their car registration number and the day of the week when this car will not be driven). In a certain family, all adults want to travel daily (each for their own business!). How many cars (at least) should the family have, if the family has a) 5 adults? b) 8 adults?