What's going on here is that this random permutation combined with the permutation of the prisoner's names in the boxes gives you a permutation of the prisoners, which is a uniformly random permutation.

What we learn is that if it can be homogeneous, if this is a homogeneous differential equation, that we can make a variable substitution.

Prompt on replace

We're asked to evaluate the expression a squared plus ten b minus eight when a is equal to seven and b is equal to negative four.

Position of the characters to replace

This is the archetype of the hard disk that's in your machine now.

Like somehow you could be replaced

Let me put the Laplace transform of and I'm also going to the sides.

It will render them right in place here.

Now we know what g of 3 is equal to.

We could do no correction at all we have to consider that as one of the possibilities.

So the opposite is u prime v.

And the worst thing? It's all done in secret.

Using what I described in the previous slide what we're just talking about, you can actually patch this up by moving the 50 around doing some various swaps.

Replace with

Replace With

And this is just the same thing as x minus y squared.

Replacing string.

Now this might look a little bit bizarre to you, but if you made a substitution right here, if you said that x is equal to ad, and if you said y is equal to cb, then what does this become?

If you press the Replacebutton, the text you entered above is searched for within the document and any occurrence is replaced with the replacement text.

Because we were able to write it as a function of y divided by x.

This option, pplus goes to P, corresponds to picking just one.

So f of 5 is equal to 5 plus 3 times g of 5, right?

It's very ironic. And I'll show you a little natural recursion here.

Laplace transform of e to the at.

It is very pink and very yellow.

Using these rules, if I start with sentence,

Part of text you want to replace

New text which will be replacement

Text which you want to replace some characters

Number of characters to replace

That means the heap property isn't satisfied but all we have to do to fix it is we just swap the value in the left child and i.

Replace All

This is the sequential game in extensive form.

Replace

Replace...

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Replace

Replace

Contiguous Fill

Row replacement

Replacement

Even on the first view, your eyes will successfully pick out patterns, but on repeated views, your brain actually gets better at turning these patterns into information.

Replacements and exceptions for language

with