A Tail?

Touch the middle part of one rod with another.

If the rod that you hold is a magnet, it will be attracted strongly and will stick with the other rod.
If the rod that you hold is not a magnet, the attraction will be much less (depends on the sizes). This is because, the magnetic field at the centre of a magnet is weak.

One obvious route is for the ant to crawl along the line of contact between the box and the floor.
This is clearly 25 + 36 = 61 cm in length.

Can the ant find a shorter path by crawling over the top of the box?

The key insight is to flatten the box.  Having done this, it’s clear that the shortest path must be one of the straight line paths from one corner to its opposite.  There are four such paths.  They are the diagonals of:

• • a 36 by 12+25+12 cm rectangle

• • a 25 by 12+36+12 cm rectangle

• • two 12+25 by 12+36 cm rectangles

Using Pythagoras’ Theorem, the lengths of these diagonals are, respectively, the square roots of 3697, 4225, and 3673.  Note that 61² = 3721, and so the path along the line of contact between the box and the floor is longer than all but one of these diagonals.

The shortest path over the box is therefore cm, or a little over 60.6 cm.

Jacob takes a piece of fruit from the box with the labels ‘Apples and Pears‘.
If it is an apple, then the label ‘Apples’ belong to this box.
The box that said ‘Apples’, then of course shouldn’t be labeled ‘Apples and Pears‘, because that would mean that the box with ‘Pears’ would have been labeled correctly, and this is contradictory to the fact that none of the labels was correct.
On the box with the label ‘Appels’ should be the label ‘Pears’.

If Jacob would have taken a pear, just replace ‘Apples’ with ‘Pears’ in the above solution

Take 4 tens

Obviously if you choose a royal flush, your opponent could match you with one of her own. Picking 4 Aces and a King, say, could be answered by 4 Queens and another card. You could then discard all 5 cards and draw a Jack-high straight flush. But your opponent could beat you with a Queen-high straight flush. If you draw so as to prevent a Queen-high straight flush your opponent stands pat and beats you with 4 Queens.

If you select 4 10’s and another card, the best your opponent can do is a 9-high straight flush. Any selection your opponent makes allows you either a royal flush or a 10-high straight flush.

Other winning combinations are 3 10’s and A-9, K-9, Q-9, J-9, K-8, Q-8, J-8, J-7, or J-6 in the fourth suit.

With only two fuses that burn exactly one hour, one can measure three quarters of an hour accurately, by lighting the first fuse at both ends and the other fuse at one end simultaneously.
When the first fuse is burnt out after exactly half an hour you know that the second fuse still has exactly half an hour to go before it will be burnt completely, but we won’t wait for that.
We will now also light the other end of the second fuse.
This means that the second fuse will now be burnt completely after another quarter of an hour, which adds up to exactly three quarters of an hour since we started lighting the first fuse!

No, it is not possible to cut the chessboard paper into pieces such that each piece has twice as much squares of one color than of the other color.

If it would be possible, then every piece would have a number of squares divisible by 3 (because if a piece has n squares of one color and 2×n squares of the other color, it has 3×n squares in total).
The total number of squares of all pieces would then also be divisible by 3.
This is, however, impossible since the total number of squares on the chessboard is 64, which is not divisible by 3.

Ask anyone, “Which way goes to your city ?”.

Explanation:
The person belonging to City of Truth  always tells the truth and will tell you the way to his city, while the person belonging to City of Lies  will lie and point in the direction of City of Truth.
Hence, in both ways you will know the direction to the City of Truth.

A Tetrahedron is the polyhedron where all points are equidistant to each other.
So the man should grow the plants such that they form the tetrahedron.
For ex: 3 plants at the base and 1 at the top of the mountain.

Simply invert an equilatetal tetrahedron.
Plant 3 plants in an equilateral triangle, then dig a hole in the center such that the base of the hole is the same distance from each of the 3 previous plants as they are from each other.
Then plant the fourth plant at the base of the hole.

Towel