What are the eight coins you need to take, so that you can use them to pay without change any amount from 1 pence up to 1 pound?
(In circulation at the time, there were coins of 1, 3, 5, 10, 20 and 50 pence).
The director of a power plant, considering the list of phone numbers and the names of his employees, noticed a certain relationship between names and phone numbers. Here are some names and phone numbers from the list:
Achinskiy 9125
Butenko 7215
Dapin 5414
Galick 6711
Martyanof 9136
Romidze 7185
What is the phone number of an employee named Ognef?
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?
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.
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?
Three friends – Peter, Ryan and Sarah – are university students, each studying a different subject from one of the following: mathematics, physics or chemistry. If Peter is the mathematician then Sarah isn’t the physicist. If Ryan isn’t the physicist then Peter is the mathematician. If Sarah isn’t the mathematician then Ryan is the chemist. Can you determine which subject each of the friends is studying?
A square piece of paper is cut into 6 pieces, each of which is a convex polygon. 5 of the pieces are lost, leaving only one piece in the form of a regular octagon (see the drawing). Is it possible to reconstruct the original square using just this information?