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Reed Nelson committed Oct 15, 2023
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2 changes: 1 addition & 1 deletion readme.md
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Expand Up @@ -10,7 +10,7 @@ Clone: `git clone https://github.com/reednel/pages.git`

Checkout template: `git checkout template`

Use Node 20: `nvm install --lts`
Use Node 20: `nvm install 20`

Install Node Modules: `npm install`

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1 change: 0 additions & 1 deletion src/content/about/-index.md
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Expand Up @@ -2,7 +2,6 @@
title: About
meta_title: About
description: About Reed Nelson.
image: /assets/about/reed.jpg
draft: false
---

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8 changes: 4 additions & 4 deletions src/content/blog/debruijn.md
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Expand Up @@ -28,7 +28,7 @@ Let $A$ be an alphabet of $k$ distinct characters[^2]. A **de Bruijn sequence**

Each $B(k, n)$ has a corresponding de Bruijn graph. The example in the figure below shows the graph for $B(2, 3)$.

![B(2, 3) Graph](/assets/blog/debruijn/b23_graph.png)
![B(2, 3) Graph](@assets/blog/debruijn/b23_graph.png)

**De Bruijn graphs** are directed Eulerian graphs, which is to say that there exists a circuit (connected loop) within the graph which visits each *edge* exactly once. These graphs have a number of interrelated properties.

Expand All @@ -40,7 +40,7 @@ Each $B(k, n)$ has a corresponding de Bruijn graph. The example in the figure be

**Property 6:** Because each vertex has exactly $k$ incoming and outgoing edges, the number of edges of $B(k, n)$ are $k\cdot k^{n-1}$, or $k^n$. Notice that $B(k, n+1)$ has a number of vertices equal to the number of edges of $B(k, n)$. We can draw the graph for $B(k, n+1)$ in the following way: put a vertex where each edge of $B(k, n)$ would be, whose label is the character on that edge, concatenated to the source vertex. In this way, each vertex remains unique with respect to all other vertices in the $B(k, n+1)$ graph. Applying this method to the $B(2, 3)$ graph pictured above yields the $B(2, 4)$ graph pictured in the figure below. This tracks with Property 4.

![B(2, 4) Graph](/assets/blog/debruijn/b24_graph.png)
![B(2, 4) Graph](@assets/blog/debruijn/b24_graph.png)

**Property 7:** By following an Eulerian circuit through a $B(k, n-1)$ graph, and recording the label of each edge as it is visited, one gets a $B(k, n)$ sequence. Furthermore, the set of sequences constructed by taking all Eulerian circuits in the $B(k,n-1)$ graph is identical to the set of $B(k, n)$ sequences. This fact is key in creating a generating algorithm.

Expand All @@ -58,7 +58,7 @@ The $B(k, n)$ graph will be represented by an adjacency matrix[^4]. The data str

Each vertex (a value in base-$k$) corresponds to the index of that value in decimal. Then whether one vertex points to another (or the same) depends on if the rightmost $n-1$ characters of the row index are the same as the leftmost $n-1$ characters of the column index (in the spirit of the example described in Property 5). The adjacency matrix corresponding to the $B(2, 3)$ graph is pictured in the figure below, and can be verified by examining the first figure.

![B(2, 3) Adjacency Matrix](/assets/blog/debruijn/b23_adjmatrix.png)
![B(2, 3) Adjacency Matrix](@assets/blog/debruijn/b23_adjmatrix.png)

### Traversing the Graph

Expand Down Expand Up @@ -103,7 +103,7 @@ $\underline{01234}56789 \to \underline{0}5\underline{1}6\underline{2}7\underline

Below are some results from a function which checks each rotation of each sequence provided by the generator, and returns those which out-shuffle.

![Sample out-shuffling de Bruijn sequences](/assets/blog/debruijn/b_outshuffles.png)
![Sample out-shuffling de Bruijn sequences](@assets/blog/debruijn/b_outshuffles.png)

There would be a number of interesting directions to take this shuffling idea. The naive method for checking if a sequence can shuffle to itself would be $O(n^2)$ with respect to the length of the sequence: for each of $n$ rotations, you compare the character at each index of the original sequence to the character at each index of the transformed sequence. I wonder if it's possible to tell whether some rotation of a sequnce will shuffle, just by examining a single rotation. One might also be able to take this in an algebraic direction: perhaps the right sets of sequences shuffle to each other, forming a [group](https://en.wikipedia.org/wiki/Group_theory) under shuffling operation.

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2 changes: 1 addition & 1 deletion src/content/blog/huffman.md
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Expand Up @@ -58,7 +58,7 @@ In the 50's, MIT PhD student David Huffman had to write a paper proving some cod

5. Build a binary tree for which all the leaves are the original members of $\Omega$, and two nodes share a parent if they were replaced by that parent in step (2).

![Visualization of the Huffman Coding algorithm](/assets/blog/huffman/huffman.png)
![Visualization of the Huffman Coding algorithm](@assets/blog/huffman/huffman.png)

Huffman's simple $O(n\log(n))$ algorithm finds an optimal symbol-by-symbol coding. There are alternate methods of coding which perform better under certain circumstances, but even where suboptimal, Huffman is quite good.

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10 changes: 5 additions & 5 deletions src/content/config.ts
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Expand Up @@ -8,8 +8,8 @@ const blogCollection = defineCollection({
description: z.string().optional(),
date: z.date().optional(),
author: z.string().default("Reed Nelson"),
categories: z.array(z.string()).default(["others"]),
tags: z.array(z.string()).default(["others"]),
categories: z.array(z.string()).default(["none"]),
tags: z.array(z.string()).default(["none"]),
complexity: z.number().default(1),
draft: z.boolean().optional(),
}),
Expand All @@ -27,13 +27,13 @@ const puzzleCollection = defineCollection({

// Drink collection schema
const drinkCollection = defineCollection({
schema: z.object({
schema: ({ image }) => z.object({
title: z.string(),
meta_title: z.string().optional(),
description: z.string().optional(),
date: z.date().optional(),
image: z.string().optional(),
author: z.string().default("Admin"),
cover: image().optional(),
author: z.string().default("none"),
spirits: z.array(z.string()).default(["none"]),
bottles: z.array(z.string()).default(["none"]),
tags: z.array(z.string()).default(["none"]),
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2 changes: 1 addition & 1 deletion src/content/drink/_drink.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Drink
author: Reed Nelson
draft: true
description: recipe.
image: /assets/drink/.jpg
cover: "@assets/drink/.jpg"

spirits: [spirit]
bottles: [bottle]
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2 changes: 1 addition & 1 deletion src/content/drink/amaretto-sour.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Amaretto Sour
author: Reed Nelson
draft: false
description: Amaretto Sour recipe.
image: /assets/drink/amaretto-sour.jpg
cover: "@assets/drink/amaretto-sour.jpg"

spirits: [whiskey]
bottles: [amaretto]
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2 changes: 1 addition & 1 deletion src/content/drink/appley-cocktail.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Appley Cocktail
author: Reed Nelson
draft: false
description: Appley Cocktail recipe.
image: /assets/drink/appley-cocktail.jpg
cover: "@assets/drink/appley-cocktail.jpg"

spirits: [whiskey]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/basilica.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Basilica
author: Reed Nelson
draft: false
description: Basilica recipe.
image: /assets/drink/basilica.jpg
cover: "@assets/drink/basilica.jpg"

spirits: [gin]
bottles: [ango, st-germain]
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2 changes: 1 addition & 1 deletion src/content/drink/berlin.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Berlin
author: Reed Nelson
draft: false
description: Berlin recipe.
image: /assets/drink/berlin.jpg
cover: "@assets/drink/berlin.jpg"

spirits: [whiskey]
bottles: [sweet-vermouth, benedictine]
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2 changes: 1 addition & 1 deletion src/content/drink/boulevardier.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Boulevardier
author: Reed Nelson
draft: false
description: Boulevardier recipe.
image: /assets/drink/boulevardier.jpg
cover: "@assets/drink/boulevardier.jpg"

spirits: [whiskey]
bottles: [sweet-vermouth, campari]
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2 changes: 1 addition & 1 deletion src/content/drink/bourbon-bash.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Bourbon Bash
author: Reed Nelson
draft: false
description: Bourbon Bash recipe.
image: /assets/drink/bourbon-bash.jpg
cover: "@assets/drink/bourbon-bash.jpg"

spirits: [whiskey]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/clark-old-fashioned.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Clark Old Fashioned
author: Reed Nelson
draft: false
description: Clark Old Fashioned recipe.
image: /assets/drink/clark-old-fashioned.jpg
cover: "@assets/drink/clark-old-fashioned.jpg"

spirits: [brandy]
bottles: [ango]
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2 changes: 1 addition & 1 deletion src/content/drink/cosmopolitan.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Cosmopolitan
author: Reed Nelson
draft: false
description: Cosmopolitan recipe.
image: /assets/drink/cosmopolitan.jpg
cover: "@assets/drink/cosmopolitan.jpg"

spirits: [vodka]
bottles: [cointreau]
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2 changes: 1 addition & 1 deletion src/content/drink/cucumber-martini.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Cucumber Martini
author: Reed Nelson
draft: false
description: Cucumber Martini recipe.
image: /assets/drink/cucumber-martini.jpg
cover: "@assets/drink/cucumber-martini.jpg"

spirits: [vodka]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/elderflower-martini.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Elderflower Martini
author: Reed Nelson
draft: false
description: Elderflower Martini recipe.
image: /assets/drink/elderflower-martini.jpg
cover: "@assets/drink/elderflower-martini.jpg"

spirits: [vodka]
bottles: [st-germain]
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2 changes: 1 addition & 1 deletion src/content/drink/floradora.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Floradora
author: Reed Nelson
draft: false
description: Floradora recipe.
image: /assets/drink/floradora.jpg
cover: "@assets/drink/floradora.jpg"

spirits: [gin]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/gin-buck.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Gin Buck
author: Reed Nelson
draft: false
description: Gin Buck recipe.
image: /assets/drink/gin-buck.jpg
cover: "@assets/drink/gin-buck.jpg"

spirits: [Gin]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/gin-gin-mule.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Gin Gin Mule
author: Reed Nelson
draft: false
description: Gin Gin Mule recipe.
image: /assets/drink/gin-gin-mule.jpg
cover: "@assets/drink/gin-gin-mule.jpg"

spirits: [Gin]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/hotel-georgia.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Hotel Georgia
author: Reed Nelson
draft: false
description: Hotel Georgia recipe.
image: /assets/drink/hotel-georgia.jpg
cover: "@assets/drink/hotel-georgia.jpg"

spirits: [gin]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/improved-japanese-cocktail.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Improved Japanese Cocktail
author: Reed Nelson
draft: false
description: Improved Japanese Cocktail recipe.
image: /assets/drink/improved-japanese-cocktail.jpg
cover: "@assets/drink/improved-japanese-cocktail.jpg"

spirits: [brandy]
bottles: [peychauds]
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2 changes: 1 addition & 1 deletion src/content/drink/improved-whiskey-cocktail.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Improved Whiskey Cocktail
author: Reed Nelson
draft: false
description: Improved Whiskey Cocktail recipe.
image: /assets/drink/improved-whiskey-cocktail.jpg
cover: "@assets/drink/improved-whiskey-cocktail.jpg"

spirits: [whiskey]
bottles: [maraschino, absinthe]
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2 changes: 1 addition & 1 deletion src/content/drink/irish-maid.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Irish Maid
author: Reed Nelson
draft: false
description: Irish Maid recipe.
image: /assets/drink/irish-maid.jpg
cover: "@assets/drink/irish-maid.jpg"

spirits: [whiskey]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/kentucky-maid.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Kentucky Maid
author: Reed Nelson
draft: false
description: Kentucky Maid recipe.
image: /assets/drink/kentucky-maid.jpg
cover: "@assets/drink/kentucky-maid.jpg"

spirits: [whiskey]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/la-louisiane.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: La Louisiane
author: Reed Nelson
draft: false
description: La Louisiane recipe.
image: /assets/drink/la-louisiane.jpg
cover: "@assets/drink/la-louisiane.jpg"

spirits: [whiskey]
bottles: [peychauds, sweet-vermouth, benedictine, absinthe]
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2 changes: 1 addition & 1 deletion src/content/drink/lemon-drop-martini.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Lemon Drop Martini
author: Reed Nelson
draft: false
description: Lemon Drop Martini recipe.
image: /assets/drink/lemon-drop-martini.jpg
cover: "@assets/drink/lemon-drop-martini.jpg"

spirits: [vodka]
bottles: [cointreau]
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2 changes: 1 addition & 1 deletion src/content/drink/london-gypsy.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: London Gypsy
author: Reed Nelson
draft: false
description: London Gypsy recipe.
image: /assets/drink/london-gypsy.jpg
cover: "@assets/drink/london-gypsy.jpg"

spirits: [gin]
bottles: [ango, benedictine]
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2 changes: 1 addition & 1 deletion src/content/drink/lucien-gaudin.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Lucien Gaudin
author: Reed Nelson
draft: false
description: Lucien Gaudin recipe.
image: /assets/drink/lucien-gaudin.jpg
cover: "@assets/drink/lucien-gaudin.jpg"

spirits: [gin]
bottles: [dry-vermouth, campari, cointreau]
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2 changes: 1 addition & 1 deletion src/content/drink/manhattan.md
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Expand Up @@ -2,7 +2,7 @@
title: Manhattan
meta_title: Manhattan
description: Manhattan recipe.
image: /assets/drink/manhattan.jpg
cover: "@assets/drink/manhattan.jpg"
author: Reed Nelson
draft: false

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2 changes: 1 addition & 1 deletion src/content/drink/martinez.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Martinez
author: Reed Nelson
draft: false
description: Martinez recipe.
image: /assets/drink/martinez.jpg
cover: "@assets/drink/martinez.jpg"

spirits: [gin]
bottles: [ango, sweet-vermouth, maraschino]
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2 changes: 1 addition & 1 deletion src/content/drink/martini.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Martini
author: Reed Nelson
draft: false
description: Martini recipe.
image: /assets/drink/martini.jpg
cover: "@assets/drink/martini.jpg"

spirits: [gin]
bottles: [dry-vermouth, orange-bitters]
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2 changes: 1 addition & 1 deletion src/content/drink/mojito.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Mojito
author: Reed Nelson
draft: false
description: Mojito recipe.
image: /assets/drink/mojito.jpg
cover: "@assets/drink/mojito.jpg"

spirits: [rum]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/negroni.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Negroni
author: Reed Nelson
draft: false
description: Negroni recipe.
image: /assets/drink/negroni.jpg
cover: "@assets/drink/negroni.jpg"

spirits: [gin]
bottles: [campari, sweet-vermouth]
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2 changes: 1 addition & 1 deletion src/content/drink/new-york-sour.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: New York Sour
author: Reed Nelson
draft: false
description: New York Sour recipe.
image: /assets/drink/new-york-sour.jpg
cover: "@assets/drink/new-york-sour.jpg"

spirits: [whiskey]
bottles: [red-wine]
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2 changes: 1 addition & 1 deletion src/content/drink/old-fashioned.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Old Fashioned
author: Reed Nelson
draft: false
description: Old Fashioned recipe.
image: /assets/drink/old-fashioned.jpg
cover: "@assets/drink/old-fashioned.jpg"

spirits: [whiskey]
bottles: [ango]
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2 changes: 1 addition & 1 deletion src/content/drink/orange-bite.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Orange Bite
author: Reed Nelson
draft: false
description: Orange Bite recipe.
image: /assets/drink/orange-bite.jpg
cover: "@assets/drink/orange-bite.jpg"

spirits: [gin]
bottles: [cointreau, orange-bitters]
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2 changes: 1 addition & 1 deletion src/content/drink/pike-bay-special.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Pike Bay Special
author: Reed Nelson
draft: false
description: Pike Bay Special recipe.
image: /assets/drink/pike-bay-special.jpg
cover: "@assets/drink/pike-bay-special.jpg"

spirits: [vodka]
bottles: [irish-cream, schnapps]
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2 changes: 1 addition & 1 deletion src/content/drink/raspberry-martini.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Raspberry Martini
author: Reed Nelson
draft: false
description: Raspberry Martini recipe.
image: /assets/drink/raspberry-martini.jpg
cover: "@assets/drink/raspberry-martini.jpg"

spirits: [vodka]
bottles: []
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2 changes: 1 addition & 1 deletion src/content/drink/raspberryy-cocktail.md
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Expand Up @@ -4,7 +4,7 @@ meta_title: Raspberryy Cocktail
author: Reed Nelson
draft: false
description: Raspberryy Cocktail recipe.
image: /assets/drink/raspberryy-cocktail.jpg
cover: "@assets/drink/raspberryy-cocktail.jpg"

spirits: [whiskey]
bottles: [peychauds]
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