[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 578

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DmitriyN: Switch on all the torches. Measure the current consumption of the torch. Measure the current consumption of all the torches. Divide the total current by the current of one torch :))))
An ammeter is probably not available.
 
Mathemat:

[Simple] What is the angle between the hands of the clock at 18:45?

The angle of the minute hand: 45/60*360=270 degrees;

Convert the time format to decimal: 18:45=6.75 hours;

Angle of the hour hand: 6.75/12*360=202.5 degrees;

Subtract angles: 270-202.5=67.5 degrees.

 
DmitriyN: Subtract the angles: 270-202.5=67.5 degrees.
Yep.
 
Mathemat:
There is probably no ammeter.
I would smash all the bulbs with a slingshot.... (counting them) or can't you smash bulbs?
 
Aleksander: I would smash all the light bulbs with a slingshot.... (counting them) or can't I smash bulbs?
A slingshot is a forbidden measuring device.
 
If someone who counts horses can detectwhether a light is on (at least one torch is on) or not, then the problem is solvable.
 

I looked up something similar to a solution on the hubrabs.

Take a light bulb - let's say, a burning one. Think of it as a Reference Point (_TO). We start stomping forward and make sure to count the steps (or rather, horses, how many have passed).

As soon as we meet a light bulb in the same state (burning), we turn it off.

After that we go back to the _TO (we know how much we've walked from it). We check whether it's on or off.

If the _TO is lit, it means that we haven't reached the end, i.e. we haven't knocked out the _TO. Again we go forward to the last one knocked out and stomp on to the next one lit. And so on.

If the _TO is off, it means that we have already bypassed the carousel.

 
Mathemat:

I looked up something similar to a solution on the hubrabs.

Take a light bulb - let's say, a burning one. Think of it as a Reference Point (_TO). We start stomping forward and make sure to count the steps.

As soon as you meet a light bulb in the same state (burning), turn it off.

After that, go back to the _TO (we know how many steps we have walked from it). We check whether it is lit or not.

If the _TO is lit, it means that we haven't reached the end, i.e. we haven't knocked out the _TO. Again we go forward to the last one knocked out and stomp on to the next one lit. And so on.

If the _TO is off, it means that we have already bypassed the carousel.


There are too many steps. In the solution I found you have to go 2 full circles.
 
The tachometer needs to be optical. Put someone on a horse and measure the frequency by pointing the tachometer at them. Then do the same with the horses. Divide the last frequency by the first frequency to get the number.
 
What's stopping you from turning off all the lights, then turning on just one and counting its TO?
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