A poetry society has 33 members, and each person knows at least 16 people from the society. Show that you can get to know everyone in the society by a series of introductions if you already know someone from the society.
Some Star Trek fans and some Doctor Who fans met at a science fiction convention. It turned out that everyone knew exactly three people at the convention. However, none of the Star Trek fans knew each other and none of the Doctor Who fans knew each other. Show that there are the same number of Star Trek fans as the number of Doctor Who fans at the convention.
Starting at one of the vertices, an ant wishes to walk each of the
Noah has
The alsatian is the least picky and can be paired with any in the second group.
The border collie won’t go with the foxhound, but will go with any other dog in the second group.
The chihuahua and the dachshund will only go with the Irish setter and the Jack Russell.
Additionally, none of the foxhound, greyhound and harrier will go with the English bulldog.
Is it possible to pair up the
Multiply an odd number by the two numbers either side of it. Prove that the final product is divisible by
Mattia is thinking of a big positive integer. He tells you what this number to the power of
You might want to know what day of the week your birthday is this year. Mathematician John Conway invented an algorithm called the ‘Doomsday Rule’ to determine which day of the week a particular date falls on. It works by finding the ‘anchor day’ for the year that you’re working in. For
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Then find the nearest one of these dates to the date that you’re looking for and find remainders.
For example,
What day of the week will
That is, we count A,B,C vs. D,E,F as the same splitting as F,D,E vs A,C,B.
Picasso colours every point on the circumference of a circle red or blue. Is he guaranteed to create an equilateral triangle all of whose vertices are the same colour?
Let