# Posts for Tag: math

### Interactive Spirograph

Posted In: Fun | Math

Play with an interactive spirograph and share your creations with your friends. Just play around with the controls at the top and see what interesting designs you can come up with.

Instructions
Wheel Size controls the size of the wheel inside the ring
Hole Distance controls the distance from the center of the wheel and the edge
Drawing Speed controls the speed at which the spirograph is spins
Line Thickness controls the thickness of the line on the drawing
Line Color is a color picker letting you change the color of the lines
Show Ring and Wheel lets you toggle whether the Ring and Wheel are showing
Clear erases the design
generates a custom URL and copies it to the clipboard so you can share this exact design with your friends.
/ allows you to start and stop the spirograph animation

Equations
The spirographs shown here are hypotrochoids, which is described as a curve generated by tracing a point attached to a circle that rolls around the interior of a larger circle. The equations for the curve are:
\begin{aligned}&x(\theta )=(R-r)\cos \theta +d\cos \left({R-r \over r}\theta \right)\\&y(\theta )=(R-r)\sin \theta -d\sin \left({R-r \over r}\theta \right)\end{aligned}

Sources and Tools
The equations for the spirograph hypotrochoids are from Wikipedia. The drawings and UI are made using canvas and HTML/Javascript and CSS.

### NY Times Digits Archive

Posted In: Fun | Game | Math
You can also play new daily Digits puzzles and try out the Digits Solver

#### You can still play the NYT Digits Game

Missing the NYT Digits game? You can still play (or replay) the old puzzles here.

On August 8th, 2023, the New York Times ended the beta for their Digits math game and the game is no longer playable. The game ran from April 10th to August 8th and there were 120 different daily puzzles during that time.

Twitter user @Digits_Analysis had compiled a list of each of the five daily puzzles during that entire time period (600 puzzles total) and generously provided them to me. Since I already coded up a Digits replacement with daily puzzles, I figured I could adapt that code fairly easily to make a version where you could play old puzzles. The first 120 puzzles are the original NY Times puzzles and subsequent puzzles are the collection of new daily puzzles.

#### Rules

The rules for Digits are relatively simple just like in the NYT version. Each day’s puzzle has 5 individual puzzles to complete. Every puzzle has a target number and 6 individual starting numbers that you must use in mathematical calculations to try and create the target number. Each of the 6 numbers can only be used once but the answer to a given math calculation becomes a new number to use.

Once you finish one puzzle, you can use the tabs at the top to move to another puzzle.

#### Scoring

You get up to 3 stars for each puzzle:
3 stars if you match the target
2 stars if your number is within 10 of the target
1 star if your number is within 25 of the target

#### Other

Auto-Advance – Click on the gear to toggle on and off “auto-advance”. When enabled, the game will cue up the next puzzle if you hit the target.

Chainmode – Click on the gear to toggle on and off “chainmode”. When enabled, it will automatically highlight the answer from the previous calculation to be the first number in the new calculation.

Share – Share your Digits stars on social media using the share button, which will copy your results to your clipboard. It will share a link to the specific puzzle you are on.

# button – clicking the # button lets you see the total number of possible solutions as well as the fewest and most operations that can yield a solution. This can bring an extra element of challenge to the game. See if you can achieve the shortest solution and then try again to achieve the longest solution. Clicking on the buttons reveals one of the solutions that have the fewest and most number of operations.

Tracking your plays – Digits archive will keep track of your stars for all of 120 daily puzzles. Given that there are 120 old Digits puzzles to play, it may take folks many days, weeks or even months to go through these puzzles. One issue is that on the Safari browser on Macs and iOS devices, the data storage used to track your progress through these puzzles may be deleted if you don’t play the game for 7 days. The browser does this for privacy concerns. Just be aware that your data could be deleted by the browser if you are using Safari and don’t play at least once for 7 straight days. This shouldn’t be a problem for other browsers.

Hopefully you’ll find this enjoy playing the old NYTimes Digits math game and find it a fun and interesting way to improve your mathematical thinking. Let me know if you find any bugs or have any suggestions.

Tools
Python code was used to generate the puzzles and the game play and visuals were created in javascript, CSS and HTML. The New York Times Digits puzzle data was obtained from @Digits_Analysis

### Digits Game NYT – A Daily Math Puzzle

Posted In: Game | Math
You can now play past NYT Digits puzzles at the Digits Archive and use the Digits Solver
Press the # symbol to see the solutions.

Please share Digits with your friends, family, colleagues, math teachers, students and anyone else you think might enjoy this math puzzle game

It’s great to hear from all the folks who have taken the time to play Digits and let me know. I’m glad that so many people are enjoying it.

#### You can still play the NYT Digits Game

Missing the NYT Digits game? You can still play it here.

On August 8th, 2023, the New York Times ended the beta for their Digits math game and the game is no longer playable. About a week prior to that, a friend asked me to create a clone of Digits so he and his daughter could keep playing together. I had never played before but tried it out. Not surprisingly, since I like games, puzzles and math, I found it to be quite fun. I’m always looking out for interesting things to make, so I figured it would be a fun challenge. I’d previously made some variants of the popular Wordle Game: Wordguessr, Tridle and Scrabwordle.

#### Rules

The rules for Digits are relatively simple just like in the NYT version. Each day you are given 5 puzzles to complete. Every puzzle has a target number and 6 individual starting numbers that you must use in mathematical calculations to try and create the target number. Each of the 6 numbers can only be used once but the answer to a given math calculation becomes a new number to use.

Once you finish one puzzle, you can use the tabs at the top to move to another puzzle.

#### Scoring

You get up to 3 stars for each puzzle:
3 stars if you match the target
2 stars if your number is within 10 of the target
1 star if your number is within 25 of the target

#### Other

Auto-Advance – Click on the gear to toggle on and off “auto-advance”. When enabled, the game will cue up the next puzzle if you hit the target.

Chainmode – Click on the gear to toggle on and off “chainmode”. When enabled, it will automatically highlight the answer from the previous calculation to be the first number in the new calculation.

Share – Share your Digits stars on social media using the share button, which will copy your results to your clipboard.

# button – clicking the # button lets you see the total number of possible solutions as well as the fewest and most operations that can yield a solution. This can bring an extra element of challenge to the game. See if you can achieve the shortest solution and then try again to achieve the longest solution. Clicking on the buttons reveals one of the solutions that have the fewest and most number of operations.

Hopefully you’ll find this replacement to the NYTimes Digits math game a fun and interesting game and improve your mathematical thinking. Let me know if you find any bugs or have any suggestions.

#### Why did the New York Times discontinue Digits?

I’m guessing it wasn’t as popular as some of their other games. Wordle and the crossword puzzle are probably the most popular. And they seem to be pushing their new game Connections as a sort of replacement for Digits. But alot of folks like math games so it’s a bit of a shame that they discontinued it, especially since it’s simple to learn how to play but can be challenging to get the solution each time.

Tools
Python code was used to generate the puzzles and the game play and visuals were created in javascript, CSS and HTML.

### Interactive Dot Illusion (Individual Linear Motion Yields Circular Motion)

Posted In: Fun

This post doesn’t really involve data, but I was just messing around with animation and the canvas in Javascript and decided to make this. It’s a fun little interactive web animation that makes aggregate circular motion from a bunch of dots moving in straight lines. There are no real instructions except to mess with the controls and see what it does to the animation (i.e. change the number of dots, the speed slider, the dot colors, and show the dot paths).
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