finish exercise 1

exercises/01.managing-ui-state/02.solution.control/README.mdx

@@ -1 +1,9 @@
 # Controlling Inputs
+
+👨‍💼 Great! Now you can add/remove each of these tags to the search when they're
+checked. Programmatically controlling the input value is why you use the `value`
+prop.
+
+But the feature is incomplete because a user could manually type the tag into
+the search input and it would not be reflected in the checkbox. Let's look at
+that next.

exercises/01.managing-ui-state/03.problem.derive/README.mdx

@@ -1 +1,70 @@
 # Derive State
+
+🦉 Often, it can be easy to think you need to keep track of two elements of
+state when you really only need one. For example, let's say you have a counter
+that will display the number of times a user has clicked a button and also it
+will display whether that number is odd or even. You might be tempted to write
+the following code:
+
+```tsx
+import { useState } from 'react'
+
+export default function Counter() {
+	const [count, setCount] = useState(0)
+	const [isEven, setIsEven] = useState(true)
+
+	function handleClick() {
+		const newCount = count + 1
+		setCount(newCount)
+		setIsEven(newCount % 2 === 0)
+	}
+
+	return (
+		<div>
+			<p>{count}</p>
+			<p>{isEven ? 'Even' : 'Odd'}</p>
+			<button onClick={handleClick}>Increment</button>
+		</div>
+	)
+}
+```
+
+This code works, but it's not ideal because it's keeping track of two pieces of
+state when it only needs to keep track of one. Imagine if we had multiple places
+where the count could be changed. We'd have to remember to update the `isEven`
+state in all of those places. This is a recipe for bugs.
+
+Instead, we can derive the `isEven` state from the `count` state:
+
+```tsx
+import { useState } from 'react'
+
+export default function Counter() {
+	const [count, setCount] = useState(0)
+
+	function handleClick() {
+		const newCount = count + 1
+		setCount(newCount)
+	}
+
+	// this is the derived state
+	const isEven = count % 2 === 0
+
+	return (
+		<div>
+			<p>{count}</p>
+			<p>{isEven ? 'Even' : 'Odd'}</p>
+			<button onClick={handleClick}>Increment</button>
+		</div>
+	)
+}
+```
+
+This is a much better solution because we only have to keep track of the `count`
+state. The `isEven` state is derived from the `count` state. This means we don't
+have to worry about keeping the `isEven` state in sync with the `count` state.
+
+👨‍💼 Thanks Olivia! So what we want to do in this step is derive the checkboxes'
+`checked` state based on whether the query contains the word they represent.
+
+Give that a shot.

exercises/01.managing-ui-state/03.solution.derive/README.mdx

@@ -1 +1,5 @@
 # Derive State
+
+👨‍💼 Awesome work! It looks really cool to have the checkboxes check and uncheck
+automatically as you type! We're now controlling both all the inputs on here
+all based on a single element of state. Well done.

exercises/01.managing-ui-state/04.problem.init/README.mdx

@@ -1 +1,20 @@
 # Initialize State
+
+👨‍💼 We want users to be able to share a link to this page with a prefilled
+search. For example:
+[`https://www.example.com/search?query=cat+dog`](/app/playground?query=cat+dog).
+
+Right now, this won't work, because we don't have a way to initialize the
+state of the search box from the URL. Let's fix that.
+
+The `useState` hook supports an initial value. Right now we're just passing
+`''` as the initial value, but we can use the `URLSearchParams` API to get the
+query string from the URL and use that as the initial value.
+
+```tsx
+const params = new URLSearchParams(window.location.search)
+const initialQuery = params.get('query') ?? ''
+```
+
+Then you can pass that `initialQuery` to `useState`. Give that a shot and then
+the link above should work!