Logical & Mathematical Puzzles

i. Growing Water-Lily

In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily.

The Question: After how many days will half of the pool be covered by the water-lily?

ii. Traveling Bird

Consider a road with two cars, at a distance of 100 kilometers, driving towards each other. The left car drives at a speed of forty kilometers per hour and the right car at a speed of sixty kilometers per hour. A bird starts at the same location as the right car and flies at a speed of 80 kilometers per hour. When it reaches the left car it turns its direction, and when it reaches the right car it turns its direction again to the opposite, etcetera.

The Question: What is the total distance that the bird has traveled at the moment that the two cars have reached each other?
[Bird and 2 Cars]

iii. Cork in the Canal

A swimmer jumps from a bridge over a canal and swims 1 kilometer stream up. After that first kilometer, he passes a floating cork. He continues swimming for half an hour and then turns around and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant speed.

The Question: How fast does the water in the canal flow?

iv. Square And Rectangle

The area of the square shown below is 8 x 8 = 64. The square is cut in the four parts A, B, C, and D, which are rearranged into the rectangle shown below. This rectangle has an area of 13 x 5 = 65.

[8x8 Square]

The Question: How can you explain the difference in area?

v. Jolly Jugs

You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters.

The Question: How can you get just 4 liters of water using only these two jugs?

vi. Camel & Bananas

A banana plantation is located next to a desert. The plantation owner has 3000 bananas that he wants to transport to the market by camel, across a 1000 kilometre stretch of desert. The owner has only one camel, which carries a maximum of 1000 bananas at any moment in time, and eats one banana every kilometre it travels.

The Question: What is the largest number of bananas that can be delivered at the market?

vii. Four Flies

Consider 4 (dimensionless) flies, 2 males and 2 females. They are situated at the corners of 1 square meter. Every fly tries to reach the male/female fly in front of her/him. Their initial situation is visualized in the picture. Since the flies are flying towards another, they will meet each other at a certain time in the center of the square.

The Question: What is the length of the path they have traveled at the moment they reach each other?

[Brick-Chess board: 10x10, without two opposite corner squares!]

viii. Placing Bricks

Try to fill the total board (10x10-2) with bricks of size 2 (

and

), so no overlaps, no gaps, and no bricks crossing the borders.

The Question: Is this possible? (Proof!)

Another Question: How many squares are present in the picture of the board?

ix. Replacement Resistance

Here is a little problem from the physical/electro-technical area. Only basic knowledge about electricity and resistance is required, like:

The replacement resistance of two serial connected resistances

is 2 Ohm (i.e. adding).

The replacement resistance of two parallel connected resistances
[Parallel resistant of 1 Ohm and 1 Ohm]

is 1/2 Ohm (i.e. dividing).

The Question: What is the replacement resistance of the circuit below?

Hint: The solution is rather easy and lies in the range of [0..5].

x. Cable Curve

A cable, 16 meters in length, hangs between two pillars that are both 15 meters high. The ends of the cable are attached to the tops of the pillars. At its lowest point, the cable hangs 7 meters above the ground.

The Question: How far are the two pillars apart?

xi. The Bridge

Four men want to cross a bridge. They all begin on the same side. It is night, and they have only one flashlight with them. At most two men can cross the bridge at a time, and any party who crosses, either one or two people, must have the flashlight with them.
The flashlight must be walked back and forth: it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the speed of the slower man. Man 1 needs 1 minute to cross the bridge, man 2 needs 2 minutes, man 3 needs 5 minutes, and man 4 needs 10 minutes. For example, if man 1 and man 3 walk across together, they need 5 minutes.

The Question: How can all four men cross the bridge in 17 minutes?

xii. Coin Weighing

We have 12 coins and a balance. 11 Coins are of the same weight, but one coin differs in weight. You may perform three weighings to find out which coin has a different weight.

Note that you don't know whether the coin with different weight is heavier or lighter!

The Question: How should you do these three experiments to find it out?

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