Driver's Seat

Where is the driver sitting in this car?


Using the positioning of the mirrors, you can conclude that the driver is sitting on the right.


By the Book

Brainwright is a company known for its colorful, innovative puzzles, and "By the Book" is not an exception. The puzzle comes in a sturdy box, in which you will find small replicas of 2 shelves, 12 books, a cat, and a vase. You will also get 40 cards with various challenges on them, ordered in terms of difficulty. Each challenge requires that you arrange some subset of the books (and possibly the cat) on the lower shelf, so that afterwards the upper shelf can be placed flatly on top. This task is just as fun to do as it sounds, and the cute design of the miniatures makes the toy even harder to put down.

Unfortunately, despite the interesting idea and masterful execution of the puzzle, the challenges themselves are rather poorly designed. Most of them have multiple solutions, and even the hardest ones occasionally can be solved by using very simple logic (find two books with the same heights and place the others in-between). Also, the constraints which are included in some of the challenges, e.g. book A and book B must not touch each other, are often redundant and simply frustrating. Considering the low number of problems to solve and their overall easy difficulty, one can go through all of them within probably just an hour. 

Ultimately, it is very hard to rate "By the Book". It scores high in terms of originality, design, and sheer fun, but scores pretty low in terms of logic, which is crucial for puzzles. Overall, I think it will be a good addition to your collection, especially if you have younger children around, but don't expect any amount of challenge from it.

  • great aesthetics and built
  • interesting idea, fun to solve
  • few and poorly designed challenges
  • recommended

Students with Hats

One teacher decided to test three of his students - Frank, Gary and Henry. The teacher took three hats, wrote on each hat an integer number greater than 0, and put the hats on the heads of the students. Each student could see the numbers written on the hats of the other two students but not the number written on his own hat.
The teacher said that one of the numbers is sum of the other two and started asking the students:

-- Frank, do you know the number on your hat?
-- No, I don't.
--Gary, do you know the number on your hat?
-- No, I don't.
--Henry, do you know the number on your hat?
-- No, I don't.

Then the teacher started another round of questioning:
-- Frank, do you know the number on your hat?
-- No, I don't.
--Gary, do you know the number on your hat?
-- No, I don't.
--Henry, do you know the number on your hat?
-- Yes, it is 144.

What were the numbers which the teacher wrote on the hats?


Solution

The numbers are 36, 108, 144.

After the first round of questioning, all students knew that all three numbers were different. After Frank and Gary got questioned for the second time, Henry could conclude that his number was not two times larger or smaller than any of the other two numbers. This was all the information he had, and since he answered correctly, then he must have noticed that one of the following is correct:

  • the difference of Frank and Gary's numbers is twice the smaller one
  • the difference of Frank and Gary's numbers is half the bigger one
  • the sum of Frank and Gary's number is twice one of their numbers

The third option is impossible, since it will imply that Frank and Gary had the same numbers. The second option is impossible, because it will imply that the numbers Henry had the same number as Frank or Gary. Therefore, the three numbers were X, 3X, 4X, where 4X = 144. This implies that X = 36 and 3X = 108.