Problems

Decipher the puzzle shown in the diagram.

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?

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?

The old shoemaker Carl sewed some boots and sent his son Hans to the market to sell them for £25. Two disabled people came to the boy’s market stall (one without a left leg, the other without a right one) and was asked to sell each of them a boot. Hans agreed and sold each boot for £12.50.

When the boy came home and told the whole story to his father, Carl decided that his son should have sold the boots to the disabled buyers for less – each for £10. He gave Hans £5 and ordered him to return £2.50 to each disabled buyer.

While the boy was looking for the disabled people at the market, he saw that someone was selling sweets and as could not resist, spent £3 on sweets. After that, he found the disabled buyers and gave them the remaining money – each got £1. Returning home, Hans realised how badly he had acted. He told his father and asked for forgiveness. The shoemaker was very angry and punished his son by sending him to his room.

Sitting in his room, Hans thought about the day’s events. It turned out that since he returned £1 to each buyer, they paid £11.50 for each boot: \(12.50 - 1 = 11.50\). So, the boots cost £23: \(2 \times 11.50 = 23\). And Hans spent £3 on sweets, therefore, it total, there were £26: \(23 + 3 = 26\). But there were only £25! Where did the extra pound come from?

A three-digit number \(ABB\) is given, the product of the digits of which is a two-digit number \(AC\) and the product of the digits of this number is \(C\) (here, as in mathematical puzzles, the digits in the numbers are replaced by letters where the same letters correspond to the same digits and different letters to different digits). Determine the original number.

There is a 12-litre barrel filled with beer, and two empty kegs of 5 and 8 litres. Try using these kegs to:

a) divide the beer into two parts of 3 and 9 litres;

b) divide the beer into two equal parts.

A girl chose a 4-letter word and replaced each letter with the corresponding number in the alphabet. The number turned out to be 2091425. What word did she choose?

Replace the question marks with the appropriate letters or words:

a) r, o, y, g, b, ?, ?;

b) a, c, f, j, ?, ?;

c) one, three, five, ?,

d) A, H, I, M, O, T, U, ?, ?, ?, ?;

e) o, t, t, f, f, s, s, e, ?, ?.

A traveller rents a room in an inn for a week and offers the innkeeper a chain of seven silver links as payment – one link per day, with the condition that they will be payed everyday. The innkeeper agrees, with the condition that the traveller can only cut one of the links. How did the traveller manage to pay the innkeeper?

There are five chain links with 3 rings in each. What is the smallest number of rings that need to be unhooked and hooked together to connect these links into one chain?