[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 307
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
Можно ли вычеркнуть менее 43 чисел?
it is possible. For example, return any two prime whose product is greater than 44, say 41 and 43, and cross out their product itself 1763. If we try to return at least one more prime, e.g. 37, then we will have to cross out two more - 1517 and 1591, i.e. the minimum number, apparently, 42
The condition of the problem "two others of the remainder" implies "different from the product", but not necessarily "different".
The answer in the textbook is 43.
Shall we try to prove it - or is it the solution?
Alsu, you forgot about squares 41 and 43. You should cross them out too.
The condition of the problem "two others of the remainder" implies "different from the product", but not necessarily "different".
The answer in the textbook is 43.
Shall we try to prove it - or is it the solution?
As far as I understand it, the numbers in that sequence are different. Consequently, there are no 2 identical, i.e. no need to cross out the squares, just on the grounds that they are squares.
it is possible. For example, return any two prime whose product is greater than 44, say 41 and 43, and cross out their product itself 1763. If we try to return at least one more prime, for example 37, we should cross out 2 more - 1517 and 1591, i.e. minimal number, probably, 42
You are wrong.
43 * 45 = 1935
43 * 46 = 1978
41 * 45 = 1845
41 * 46 = 1886
41 * 47 = 1927
41 * 48 = 1968
That is, 41 and 43 have to be crossed out: 1763, 1845, 1886, 1927, 1935, 1968, 1978
No, it's not different, it's different from the piece. It's something different. I.e. 43*43 = 1849 is perfectly legitimate, but 1849*1 = 1849 is not.
There we are talking about "set of numbers" and "product of two numbers". It seemed to me that they are talking about different numbers, otherwise the set becomes infinite.
In principle, it doesn't matter. The important thing is that you should remove all numbers from 2 to 44, as it was stated at once. There is no way to remove less.
What if it is possible to cross out 42 numbers in some perverse way - not necessarily from the beginning of a natural series?
PapaYozh, what about the proof?
What if you can cross out 42 numbers in some perverse way - not necessarily from the beginning of a natural series?
The smaller the number, the more products it can participate in. So it's more efficient to cross out numbers from the beginning of the sequence. There is no point in crossing out "1", that's what you wrote about.
Yes, the solution is not very complete, to say the least. There is no mention of perversions.
Next, the promised one (8th):
== 100