Problems

How can you divide a pancake with three straight sections into 4, 5, 6, 7 parts?

Is it possible to bake a cake that can be divided by one straight cut into 4 pieces?

What is the maximum number of pieces that a round pancake can be divided into with three straight cuts?

The best student in the class, Katie, and the second-best, Mike, tried to find the minimum 5-digit number which consists of different even numbers. Katie found her number correctly, but Mike was mistaken. However, it turned out that the difference between Katie and Mike’s numbers was less than 100. What are Katie and Mike’s numbers?

The best student in the class, Katie, made up a huge number, writing out in a row all of the natural numbers from 1 to 500: \[123 \dots 10111213 \dots 499500.\] The second-best student, Tom, erased the first 500 digits of this number. What do you think, what number does the remaining number begin with?

Decipher the puzzle shown in the diagram.

Fred and George together with their mother were decorating the Christmas tree. So that they would not fight, their mother gave each brother the same number of decorations and branches. Fred tried to hang one decoration on each branch, but he needed one more branch for his last decoration. George tried to hang two toys on each branch, but one branch was empty. What do you think, how many branches and how many decorations did the mother give to her sons?

The farmer must transport across a river a wolf, a goat and a cabbage. The boat accommodates one person, and with him/her either a wolf, a goat, or a cabbage. If you leave the goat and the wolf unattended, the wolf will eat the goat. If you leave cabbage and goat without supervision, the goat will eat the cabbage. How can the farmer transport his cargo across the river?

In Neverland, there are magic laws of nature, one of which reads: “A magic carpet will fly only when it has a rectangular shape.” Frosty the Snowman had a magic carpet measuring \(9 \times 12\). One day, the Grinch crept up and cut off a small rug of size \(1 \times 8\) from this carpet. Frosty was very upset and wanted to cut off another \(1 \times 4\) piece to make a rectangle of \(8 \times 12\), but the Wise Owl suggested that he act differently. Instead he cut the carpet into three parts, of which a square magic carpet with a size of \(10 \times 10\) could be sown with magic threads. Can you guess how the Wise Owl restructured the ruined carpet?

Replace each letter in the diagram with a digit from 1 to 9 so that all the inequalities are satisfied,

and then arrange the letters in numerical order of their numerical values. What word did you get?