Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 222

 
Alexey:
If they all meet together, they'll all be a third colour.
Oh, I didn't realise there was a third colour in addition to red, yellow and blue.
 
Mathemat:

From the initial position, White and Black each made 4 moves. The position shown in the picture is obtained. What moves were made?

Yeah, that's funny.

/The correct answer was Mathemat.

 
Mathemat:

And one more at once, on the follow-up:

There are 13 yellow, 15 blue and 17 red chameleons living on the island. When two chameleons of different colours meet, they change to a third colour. In other cases, nothing happens. Can it happen that all the chameleons are the same colour?

Well, if they meet blue and red twice, you get 15 yellow, 13 blue and 15 red chameleons.

Then 15 blue chameleons find 15 yellow ones (13 yellow chameleons and 2 yellow chameleon pairs).

we get 13 blue singles, 13 blue pairs and 2 blue chameleon triples.

Some old problem, I guess.

 
ALXIMIKS:

If blue and red meet twice, you get 15 17 yellows 13 blues and 15 reds.

.....
 
ALXIMIKS: Some old problem, I guess.
Look for invariants, i.e. things that don't change when repainted.
 

This position arose after four moves were made on each side. What were these moves?

The weight is 3. The task is here.


 

In this game the last five moves (10 half moves) there were no captures and not a single pawn moved. Also, the black king has just suddenly disappeared from the board. On which square was he standing? Picture below.

The weight is 4. The problem is here.


Задачи, загадки, логические игры [Игры разума] икф
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В этой партии последние пять ходов (10 полуходов) не было взятий и ни одна пешка не сдвинулась с места. А еще с доски только что внезапно исчез черный король. На какой клетке он стоял? Рисунок.
 

From the initial position White and Black made 4 moves each. The position shown in the picture is obtained. What moves were made?

The weight is 4. The task here.

P.S. I think I already published this problem. It's all right, repetition is the mother of learning.

 
Mathemat:

This position arose after four moves were made on each side. What were these moves?


The weight is 3. The task is here.

1. Kf3 d6 2. Kd4(e5) d5 3. Kc6(e6) Fd7 4. Kd8 F:d8
 
Mathemat:

In this game the last five moves (10 half moves) there were no captures and not a single pawn moved. Also, the black king has just suddenly disappeared from the board. On which square was he standing? Picture below.

The weight is 4. The problem is here.

The king stood on /there was an answer - Mathemat/.

Reason: