6. Cipher Square (6 marks)

The ciphers 1, 2, 3, 4, 5, 6, 7, 8, and 9 must be put in the depicted square, in such a way that the sums of the numbers in each row, column, and diagonal are equal.

7. Number Net (6 marks)

The numbers 1 up to and including 8 must be put in the circles of the depicted net. However, numbers in neighboring circles must differ more than 1. So, for example, circles connected to a circle with a 4 may not contain a 3 or a 5.

The Question: How should the numbers be arranged in the circles of the

8. Little Lies (2 marks)

Richard is a strange liar. He lies on six days of the week, but on the seventh day he always tells the truth. He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."

Day 2: "Today, it's Thursday, Saturday, or Sunday."

Day 3: "I lie on Wednesday and Friday."

The Question: On which day does Richard tell the truth?

9. Barbara's Boxes (4 marks)

Barbara has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.

The Question: How many boxes has Barbara used in total?

10. At School (4 marks)

The gentlemen Dutch, English, Painter, and Writer are all teachers at the same secondary school. Each teacher teaches two different subjects. Furthermore:

Three teachers teach Dutch language

There is only one math teacher

There are two teachers for chemistry

Two teachers, Simon and mister English, teach history

Peter doesn't teach Dutch language

Steven is chemistry teacher

Mister Dutch doesn't teach any course that is tasught by Karl or Mister Painter.

The Question: What is the full name of each teacher and which two subjects does each one teach?

11. Climbing Snail (2 marks)

A snail is at the bottom of a 20 meters deep pit. Every day the snail climbs 5 meters upwards, but at night it slides 4 meters back downwards. How many days does it take before the snail reaches the top of the pit?

**Detailed solution**

6. Solution: The Question: How should the numbers be arranged in the square?

There is only 1 solution to this problem, when you leave out all rotations and mirror solutions:

7.Solution:

8. Solution:

We know that Richard tells the truth on only a single day of the week. If the statement on day 1 is untrue, this means that he tells the truth on Monday or Tuesday. If the statement on day 3 is untrue, this means that he tells the truth on Wednesday or Friday. Since Richard tells the truth on only one day, these statements cannot both be untrue. So, exactly one of these statements must be true, and the statement on day 2 must be untrue.

Assume that the statement on day 1 is true. Then the statement on day 3 must be untrue, from which follows that Richard tells the truth on Wednesday or Friday. So, day 1 is a Wednesday or a Friday. Therefore, day 2 is a Thursday or a Saturday. However, this would imply that the statement on day 2 is true, which is impossible. From this we can conclude that the statement on day 1 must be untrue.

This means that Richard told the truth on day 3 and that this day is a Monday or a Tuesday. So day 2 is a Sunday or a Monday. Because the statement on day 2 must be untrue, we can conclude that day 2 is a Monday.

So day 3 is a Tuesday. Therefore, the day on which Richard tells the truth is Tuesday.

9. Solution: By putting 8 boxes in a box, the total number of empty boxes increases by 8 - 1 = 7. If we call x the number of times that 8 boxes have been put in a box, we know that 11 + 7x = 102. It follows that x=13. In total, 11 + 13 × 8 = 115 boxes have been used.

10. Solution:

Since Peter as only one doesn't teach Dutch language, and mister Dutch doesn't teach any course that is taught by Karl or mister Painter, it follows that Peter and mister Dutch are the same person and that he is at least math teacher. Simon and mister English both teach history, and are also among the three Dutch teachers. Peter Dutch therefore has to teach next to math, also chemistry. Because Steven is also chemistry teacher, he cannot be mister English or mister Painter, so he must be mister Writer. Since Karl and mister Painter are two different persons, just like Simon and mister English, the names of the other two teachers are Karl English and Simon Painter.

Summarized:

Peter Dutch, math and chemistry.

Steven Writer, Dutch and chemistry.

Simon Painter, Dutch and history

Karl English, Dutch and history.

11. Solution

On the first day, the snail reaches a height of 5 meters and slides down 4 meters at night, and thus ends at a height of 1 meter.

On the second day, he reaches 6 m., but slides back to 2 m.

On the third day, he reaches 7 m., and slides back to 3 m.

On the fifteenth day, he reaches 19 m., and slides back to 15 m.

On the sixteenth day, he reaches 20 m., so now he is at the top of the pit!

Conclusion: The snail reaches the top of the pit on the 16th day

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