Problems

Decipher the following rebus

All the digits indicated by the letter “\(E\)” are even (not necessarily equal); all the numbers indicated by the letter \(O\) are odd (also not necessarily equal).

On the table four figures lie in a row: a triangle, a circle, a rectangle and a rhombus. They are painted in different colors: red, blue, yellow, green. It is known that the red figure lies between the blue and green figures; to the right of the yellow figure lies the rhombus; the circle lies to the right of both the triangle and the rhombus; the triangle does not lie on the edge; the blue and yellow figures are not next to each other. Determine in which order the figures lie and what colors they are.

Four friends came to an ice-rink, each with her brother. They broke up into pairs and started skating. It turned out that in each pair the “gentleman” was taller than the “lady” and no one is skating with his sister. The tallest boy in the group was Sam Smith, Peter Potter, then Luisa Potter, Joe Simpson, Laura Simpson, Dan Caldwell, Jane Caldwell and Hannah Smith. Determine who skated with whom.

Fill the free cells of the “hexagon” (see the figure) with integers from 1 to 19 so that in all vertical and diagonal rows the sum of the numbers, in the same row, is the same.

Six sacks of gold coins were found on a sunken ship of the fourteenth century. In the first four bags, there were 60, 30, 20 and 15 gold coins. When the coins were counted in the remaining two bags, someone noticed that the number of coins in the bags has a certain sequence. Having taken this into consideration, could you say how many coins are in the fifth and sixth bags?

Using five twos, arithmetic operations and exponentiation, form the numbers from 1 to 26.

Using five threes, arithmetic operations and exponentiation, form the numbers from 1 to 39.

Using five fours, arithmetic operations and exponentiation, form the numbers from 1 to 22.

Using five fives, arithmetic operations and exponentiation, form the numbers from 1 to 17.

Using five sixes, arithmetic operations and exponentiation, form the numbers from 1 to 14.