It is known that “copper” coins that are worth 1, 2, 3, 5 pence weigh 1, 2, 3, 5 g respectively. Among the four “copper” coins (one for each denomination), there is one defective coin, differing in weight from the normal ones. How can the defective coin be determined using scales without weights?
How can we divide 24 kg of nails into two parts of 9 kg and 15 kg with the help of scales without weights?
Harry, Jack and Fred were seated so that Harry could see Jack and Fred, Jack could only see Fred, and Fred could not see anyone. Then, from a bag which contained two white caps and three black caps (the contents of the bag were known to the boys), they took out and each put on a cap of an unknown color, and the other two hats remained in the sack. Harry said that he could not determine the color of his hat. Jack heard Harry’s statement and said that he did not have enough information to determine the color of his hat. Could Fred on the basis of these answers determine the color of his cap?
Five first-graders stood in line and held 37 flags. Everyone to the right of Harley has 14 flags, to the right of Dennis – 32 flags, to the right of Vera – 20 flags and to the right of Maxim – 8 flags. How many flags does Sasha have?
It is known that in January there are four Fridays and four Mondays. What day of the week is January 1st?
A class contains 38 pupils. Prove that within the class there will be at least 4 pupils born in the same month.
How, without any means of measurement, can you measure a length of 50 cm from a shoelace, whose length is \(2/3\) meters?
In the town of Ely, all the families have separate houses. On one fine day, each family moved into another, one of the houses house that used to be occupied by other families. They afterwards decided to paint all houses in red, blue or green colors in such a way that for each family the colour of the new and old houses would not match. Is this always possible to paint te houses in such a way, regardless of how families decided to move?
Find out the principles by which the numbers are depicted in the tables (shown in the figures below) and insert the missing number into the first table, and remove the extra number from the second table.
The Olympic gold-medalist Greyson, the silver-medalist Blackburn and bronze-medalist Reddick met in the club before training. “Pay attention,” remarked the black-haired one, “one of us is grey-haired, the other is red-haired, the third is black-haired. But none of us have the same colour hair as in our surnames. Funny, is not it?”. “You’re right,” the gold-medalist confirmed. What color is the hair of the silver-medalist?