Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 122
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MD, spill. I can already. I'm talking about the seven-coloured hubcaps problem.
The task of weighing can be postponed for the moment.
If you say so.
The hubcaps aren't difficult, but everyone has to count carefully. In short, the mega-brains number the colours from 0 to 7 in advance.
After placing the back one counts the sum of all caps standing in front of him and declares as "his colour" the sum in control - the remainder of the division of the sum by 7 ( C = Sum % 7; ).
Using this checksum, everyone can then calculate his own colour by adding up all those standing in front of him + all those named before him (except for the rearmost one).
If you say so.
It's not complicated with the hubcaps, but everyone has to count carefully. In short, the mega-brains number the colours from 0 to 7 in advance.
After the placing the back one counts the sum of all caps standing in front of him and declares as "his colour" the control sum - the remainder of the division of the sum by 7 ( C = Sum % 7; ).
On the basis of this checksum everyone can then calculate his own colour by adding up all those standing in front of him + all those named before him (except the rearmost one).
from 0 ? or from 1 ?
From 0. These are the remainders of division by 7, and they come in 0 to 6.
All megamoskis know the basics of number theory.
RATIONALE:
The contract is as follows. The caps are assigned the following numbers:
red - 0,
orange - 1,
yellow - 2, etc. up to purple (6).
The first one adds up all the numbers he sees in front of him. He divides the sum by 7 and names the colour that corresponds to the remainder of the division. He can't influence his life in any way, as he doesn't have any previous information.
Every next one determines his colour by counting the numbers of caps of different colours he sees and summing them up according to their numerical codes. Similarly, he calculates a similar sum for those before him, not counting the very first one. It then calculates the total of the two sums and calculates the remainder by dividing it by 7.
If the remainder does not match the remainder reported by the very first one, he supplements it to the reported one by adding the appropriate number from 0 to 6. This is his colour.
From 0. These are the remainders of division by 7, and they come in 0 to 6.
All megamoskis know the basics of number theory.
Got it
I converted the colours to numbers right away, but that's it.
from 0 ? or from 1 ?
Well, yes, the general approach is the same.
So, does anyone want to finish the balloon challenge? Reminder:
(4) There are two blue, two red and two green balls. In each colour, one of the balls is heavier than the other. All the lighter balls have the same weight, all the heavier ones have the same weight. There are also scales with two cups without weights. How many weighings are minimally needed to guarantee the determination of the heavy balls?
I think two.
Well, if you haven't googled it, post it.
Answered in private.
I am reminded of another long-standing problem, it was on quadruple time. No one let me know that they had solved it:
(3) Megamozg bought 53 packs of apple moth repellent. The product starts working three days after it is applied to the tree. However, he discovers that one of the packs is defective and also repels the fruit pollinator, without which no apples will grow. Megamogg can't risk his orchard, but he has six wild apple trees on which he can test the repellents. But after six days, the apple moth starts to go on a feeding frenzy, and there won't be much left of his orchard if he doesn't treat it. How can Mega Brain find the defective product and save his crop?
Comment: Everything has to be done (applied to the test trees) on Day 0. On Day 3, the gardener should already know everything - and immediately apply the correct products to all the trees in the garden. If he delays even for a minute - the apple moth will instantly eat everything in exactly 3 remaining days.
P.S. 2 Mischek: it doesn't seem to be sadistic, about the flowers and even quite decent in weight.
I'm reminded of another long-standing problem, it was on quadruple time. No one let me know that they had solved it:
(3) Megamozg bought 53 packs of apple moth repellent. The product starts working three days after it is applied to the tree. However, he discovers that one of the packs is defective and also repels the fruit pollinator, without which no apples will grow. Megamogg can't risk his orchard, but he has six wild apple trees on which he can test the repellents. But after six days, the apple moth starts to go on a feeding frenzy, and there won't be much left of his orchard if he doesn't treat it. How can Mega Brain find the defective product and save his crop?
Comment: Everything has to be done (applied to the test trees) on Day 0. On Day 3, the gardener should already know everything - and immediately apply the correct products to all the trees in the garden. If he hesitates even for a minute - the apple moth will instantly eat everything in exactly 3 remaining days.
P.S. 2 Mischek: it doesn't seem to be sadistic, about flowers and even quite decent in weight.
I am strongly against chemicals. Free the apple moths! The planet is on the brink of apocalypse. Under the guise of improving production, storage, living and life in general, chemistry is penetrating deeper and deeper into our bodies.
It must be stopped. Chemistry or the end, that is the choice facing us today.
// I'm blocked, sorry.