On the street, four girls are talking in a circle: Anna, Kate, Jane and Nina. The girl in the green dress (not Anna and not Kate) stands between the girl in the blue dress and Nina. The girl in the white dress stands between the girl in the pink dress and Kate. What color dress was each girl wearing?
Find a two-digit number that is 5 times the sum of its digits.
Decipher the puzzle shown in the picture. Same letters correspond to same numbers, different letters to different numbers.
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?
In the first pencil case, there is a lilac pen, a green pencil and a red eraser; in the second – a blue pen, a green pencil and a yellow eraser; in the third – a lilac pen, an orange pencil and a yellow eraser. The contents of these pencil cases are characterised by such a pattern: in every two of them exactly one pair of objects coincides in color and purpose. What should lie in the fourth pencil case, so that this pattern is preserved? (In each pencil case, there are exactly three objects: a pen, a pencil and an eraser.)
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?
Will the quotient or the remainder change if a divided number and the divisor are increased by 3 times?
Try to get one billion \(1000000000\) by multiplying two whole numbers, in each of which there cannot be a single zero.
Decipher the puzzle:
Decipher the puzzle: \(KIS + KSI = ISK\). The same letters correspond to the same numbers, different letters correspond to different numbers.