Show that there exists $i$ and $j$ with $1 \leq i<j \leq 51$ satisfying $a_i$ divides $a_j$. Let $a_1&lt;a_2&lt;...&lt;a_{51}$ be the given distinct natural numbers such that $1 \leq a_i \leq 100$  for all $i=1,2,....,51$. Then show that there exists $i$ and $j$ with $1 \leq i&lt;j \leq 51$ satisfying $a_i$ divides $a_j$.    There are $25$ primes less than $100$. So we must take the set $\{a_1,...,a_{51}\}$ such that the set does not contain all $25$ primes. Because if the set contains all $25$ primes then any number other than these prime would divisible by one of the prime. But from here I can not proceed further. Please help me to solve this.
Prove that if 51 positive integers between 1 and 100 are chosen, then one of them must divide another. Given $51$ integers $a_1, a_2, \ldots, a_{51}$ satisfying $1 \leq a_i \leq 100$. Prove that there exist $i$ and $j$ such that $a_i \mid a_j$.   I'm a little unsure how to approach this problem. Thanks for any help.
Moving Around Other creatures      You can move through a nonhostile creature's space [but] you can't willingly end your move in its space.   Is that "end your move" at the end of your turn or if you stop to attack? I had a player who wanted to move into another friendly character's space, attack a hostile, then sidestep behind a wall. What are the requirements for national parks? I'm trying to place a national park here:    But the button to create one with the Naturalist is greyed out:    I know the civopedia lists the requirements for building a national park, but they are either wrong or I'm having a hard time understanding them:   The tiles must be natural wonders, Mountains or a tile with an Appeal of Charming or better. As you can see the top are both Breathtaking and the bottom ones are part of the Great Barrier Reef wonder All four tiles must be owned by the same city. All tiles are within the boarders of Mbwila The tiles for a diamond shape. All tiles are connected close to each other in a diamond shape No tile can have an improvement or district on it. All tiles are in their initial condition.   So I'm probably missing something. Can someone tell me what's the problem? Double dual mappings Encrypting a folder I'm familiar with bitlocker, having been using it for a while, but I am looking at just encrypting a folder instead. But I just don't understand the options it's giving me.  When I right-click a folder > properties > advanced > [x] encrypt contents to secure data > OK &lt; apply > ...  I get:  () apply changes to this folder () apply changes to this folder, sub-folder and files.   This doesn't make sense to me at all, if I encrypt a folder then the whole folder, everything within it is encrypted, then why should I be given these options, how can I have a folder encrypted and files within that folder unencrypted, that seems stupid to me, it doesn't make sense at all.  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Without this header I have no definitions for useful types such as uint32_t, etc. I'm currently working on the following question:  "At least one of Plato and Democritus believed in the theory of forms. Plato believed in the theory of forms only if he was not an atomist, and Democritus was an atomist only if he did not believe in the theory of forms. Democritus was an atomist. Prove, using Natural Deduction, that Plato was not an atomist"  I have been working for quite some time to take the information and turn it into a set of literals and statements I can work with.  So far, I have got $P \lor D$,  $P \Rightarrow \lnot a$,  $D \Rightarrow A$,  $D = A$  However, I cannot seem to make these prove the statement using natural deduction, any hints? I have a folder with some directories and some files (some are hidden, beginning with dot). for d in *; do  echo $d done  will loop through all files and directories, but I want to loop only through directories. How do I do that? 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