## In This Shoe…

Fill the three missing numbers (using words) in the shoe below.

**SOLUTION**

Coming soon.

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Fill the three missing numbers (using words) in the shoe below.

Coming soon.

Your toaster is broken, so you decide to toast your bread in a pan. The pan can hold three slices of bread at a time and takes 1 minute to toast one of their sides. How much time would it take you to toast four slices of bread on both sides using the pan?

It would take you 2 minutes and 40 seconds. Label the slices with A, B, C, D, their top sides A1, B1, C1, D1, and their bottom sides A2, B2, C2, D2.

- Toast A1, B1, C1 for 40 seconds.
- Toast A2, B2, D1 for 40 seconds.
- Toast A1, C2, D2 for 20 seconds.
- Toast A2, C2, D2 for 20 seconds.
- Toast B1, C1, D1 for 20 seconds.
- Toast B2, C2, D2 for 20 seconds.

One hundred people entered a hotel that had 99 rooms, and each of them asked for their own room. In order to solve the problem, the bellboy did the following:

He asked the 100th guest to wait for a while with the 1st guest in room number 1, so that there were 2 guests inside. Then he took the 3rd guest to room number 2, the 4th guest to room number 3, and so on, until finally taking the 99th guest to room number 98. At the end he returned to room number 1 and took the 100th guest to room number 99, which was still vacant.

How could everybody get their own room?

The two people who were taken to room number 1 were guest 1 and guest 100. Thus, the 2nd guest ended up without a room.

During a trivia night, the following question appeared:

“Among the first five US presidents, Washington, Adams, Jefferson, Madison, and Monroe, there were 3 who died on the fourth of July. Can you guess which ones?”

After nobody answered the question, the following hint was given:

“These three presidents were consecutive ones.”

Then, all contestants immediately managed to answer the question. Can you?

Because of the way the question was worded, it was clear that the fifth president, James Monroe, was one of them. Otherwise, the trivia question would have been “among the first four US presidents” instead of “among the first five”. Since the three presidents that died on fourth of July were consecutive ones, they were Jefferson, Madison, and Monroe.

Partition the grid into disjoint “creatures”, according to the following rules:

- Each creature is defined as a shape of 4 connected branches that are each 1 cell wide.
- For each creature, one of the branches ends up with a HEAD (always clued) and the other three branches end up with LIMBS (whenever clued, their directions matter).
- A creature can never occupy a 2×2 region of cells and can never touch itself.

Examine the first example, then solve the other three puzzles.

The solutions are shown below.

If you make a CORRECT statement, you will get either a lollipop or a chewing gum. If you make a FALSE statement, you will get either a chocolate or a car. What statement should you make in order to get the car?

You should say “I will receive a chocolate”. This statement cannot be correct, since if it was, you would get a lollipop or a chewing gum, not a chocolate. Therefore, you will get the car.

Below each of the following Venn diagrams there are seven tiles consisting of two letters. Place each tile in a different region so that the four tiles in each circle can be rearranged to solve the corresponding clue.

The solutions are shown below.

Add the 25 letters between A and Y to the grid below. Each one should appear exactly once. When you have finished, you must be able to spell the following words moving horizontally, vertically or diagonally around the grid:

**AXIOM, BANQUET, CHOMP, FAWN, JOY, LURKED, RUN, STY, VYING**

The solution is shown below:

How many matchsticks do you need to remove so that no squares of any size remain?

Nine matchsticks are enough, as seen from the solution below.

To see that eight matchsticks are not enough, notice that removing an inner matchstick reduces the number of 1×1 squares at most by 2. Since there are 16 such small squares, in order to get rid of them all, we need to remove only inner matchsticks. However, in this case, the large 4×4 square will remain.

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