Problems

Can the following equality be true: $$K\times O\times T=A\times B\times C\times D\times E\times F$$ if you substitute the letters with the numbers from 1 to 9? Different letters correspond to different numbers.

An entire set of dominoes, except for 0-0, was laid out as shown in the figure. Different letters correspond to different numbers, the same – the same. The sum of the points in each line is 24. Try to restore the numbers.

Try to read the word in the first figure, using the key (see the second figure).

Before you is a lock “with a secret” (see the picture).

If you put the arrows on the desired letters, you will get the keyword and the lock will open. What is this word?

Dave spent the first Tuesday of the month in Bath, and the first Tuesday after the first Monday in Cardiff. The following month Dave spent the first Tuesday in London, and the first Tuesday after the first Monday in Cambridge. Can you determine what month and date Dave was in each of the cities?

Once Alice was in one of two countries – A or Z. She knows that all of the residents of country A always tell the truth, and all the inhabitants of country Z always lie. Moreover, they often go to visit each other. Can Alice, after asking a single question to the first person that she meets, find out which country she is in?

In a cup, glass, jug and jar there is milk, lemonade, cola and water. It is known that the water and the milk are not in the cup; the container with the lemonade stands between the jug and the cola container; the jar does not contain lemonade or water; the glass stands near the jar and the container with milk. Which container is filled with each of the liquids?

In the equation $101-102=1$, move one digit in such a way that that it becomes true.

When three friends – Nina, Helen and Anna – went out for a walk, they were wearing white, red and blue dresses. Their shoes were of the same three colors, but only Nina had the same shoe and dress color. At the same time, neither Helen’s dress, nor her shoes were blue, and Anna was wearing red shoes. Determine the color of the dresses and of the shoes of each friend.

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?