Fiat lux!

Gray cells

This has nothing to do with photography, but mainly with the fun of solving mental and geometric puzzles. Some are more difficult, others easier, but all of them have in common that they make us exercise our gray cells and keep our brain in shape. For some, the use of a calculator (which is part of every operating system) is recommended. All puzzles and tasks are the fruit of my gray cells, but I encourage you to freely share them around and come up with some yourself.

Lots of fun and gray cell exercise!

Stick

A metal rod is stuck into the bottom of the lake. Half of the rod sticks under the bottom of the lake, and one third of the rod is standing in the water. There are still 6 meters above the surface of the bar.

How long is the whole rod?

The solution

A tree

In the case of the tree, we measured a section of the trunk in the region of 10 cm in height, and the radius of the trunk there is uniformly 5 cm. In the following year, the height of the measured section did not increase, but the volume increased by 2x.

What is the new girth of the trunk at this location?

The solution

The house

A house stands on a quiet hill. It is 10 m long and 10 m wide. It also measures 10 m in height. It has a flat roof without eaves and with 450 inclination. During the night, a light and steady rain fell for 5 hours with no side wind and the amount of precipitation averaged 5 liters of water per square meter of surface in one hour. The water flows into the collector.

What is the roof area in square meters?
How many liters of water collected in the reservoir?

The solution

Rope

Cut 2/5 of the length of the rope and then 3/6 of the rest. We have 15 cm of rope left.

How long was the rope at the beginning?
What is the thickness of the rope?

The solution

Snowflake

A raindrop hardens from the cloud and falls towards the ground at a speed of 10 meters per second. After 3/5 of the way to the ground, it turns into a snowflake and its movement slows to 1/5 of its previous speed. 90 seconds passed from the start of the fall to the contact with the ground.

What is the height of the cloud from which the drop fell?

The solution

Scales and weights

On the left side of the balanced scale we have a ball weighing 5 kilograms, and on the right side we have two balls of different sizes, the smaller of which is 1/3 lighter than the larger.

How much do the balls on the right weigh individually?

The solution