## Math Teachers at Play (MTaP) Blog Carnival: Top Math Blog Posts!

This is the 73rd Edition of the Math Teachers at Play (MTaP) blog carnival!

Some interesting facts about 73 from Wikipedia!:

• Seventy-three is the 21st prime number. The previous is seventy-one, with which it comprises the 8th twin prime. It is also a permutable prime with thirty-seven. 73 is a star number.
• 73 is the largest minimal Primitive root in the first 100000 primes. In other words, if p is one of the first 100000 primes, then at least one of the primes 3, 5, 7, 11, 13, 17, …, 73 is a primitive root modulo p.
• 73 is the smallest prime congruent to 1 modulo 24.
• 73 is an emirp, meaning that the reverse of 73, that is, 37, is also a prime number. Interestingly, 73 is also the 21st prime number while 37 is the 12th prime number.

• Want to find 73 in other bases? Check out the Base Converter: Convert any number into any base!
• Which animal is year 1973 in the Chinese Zodiac? Check out this post on the Mathematics of Chinese Zodiac!

## Check out the following awesome blogs!

• Math Strategies
There is such an emphasis on learning math facts that our children do not spend enough time learning strategies that will help them solve math problems. Read about two types of strategies for solving math problems—working left to right and regrouping into what you know.
– Crystal Wagner
• Nim Games
This is a game that is generally used to show how math can be involved in game play. I explain the rules of the game as well as the mathematical strategy involved. There is also a script where users can compete against the computer
– Aftermath
• Show That Questions
This is a post around the questions that crop up in maths exams where students have to show something. I wrote it after I was surprised to hear some students hate it!
The Straight Lines Debate
This is a post exploring the benefits of the different methods of calculating straight lines.
• Day 85 – Related Rates
Two separate trucks carrying a very long wind turbine blade need to turn the corner. Describe how their speeds vary throughout the turn. The blog is dedicated to these types of discussion starters, at all levels.
– Curmudgeon
• The missing \$1 puzzle and more
You can read about that at the actual page it points to, http://www.homeschoolmath.net/online/favorite_challenging_puzzles.php
: )
– Maria
• Eggs in the Basket Review Game
This review game can be adapted to almost any level and any topic, yet it consistently provides a really effective way to review Algebra content.  It is a great way to review a lot of problems and have students work collaboratively while having fun – I just love hearing them explain their thought process to teammates when playing the game 🙂  With Easter almost here I thought it would be a good post to submit!
– Mary Williams
• Decimals in a One Frame
Inspired by Chris Hunter’s blog post about decimals on a ten frame, I thought it would be a great opening number talk for my decimal unit to see where my students were before starting our decimal journey.
– Kristin @MathMinds
• Counting Basics
• Circle Grid Designs
This post is part of a series of geometrical design activities in which shapes and patterns were found in grids constructed based on circles.
– Julie
• Ten Sticks to Make, Count With, and Play a Game With
Ten sticks created from common items can be just as much fun to make as well as to be used for counting by ones and tens  AND to play a game with.
– Margo Gentile
• Why I Always Lead with the Punchline
I wrote this after reading another blog about how listing objectives for the day takes the punchline out of the math class.  This blog just about my thoughts on sharing the learning objectives for the entire unit with students on the first day.
– Brooke Powers
• My Nemesis Maths
This post is about my journey as a teacher, trying to make maths relevant and enjoyable to all students when I myself had issues with enjoying maths as a student.
– Danielle Myburgh
• Quotable: Focus on Being Silent
The best way for children to build mathematical fluency is through conversation, especially one-on-one conversation with interested adults. Check out these ideas to encourage discussion-based math.
• 2048 Free Strategy Guide
Stuck at playing the popular and addictive Math game 2048? Do not worry, for after reading this Strategy Guide, your chance of winning will increase tremendously!

Math Teachers at Play is a traveling blog carnival. It moves around from month to month but its home base is http://letsplaymath.net/mtap/. From there you can visit the archives, submit your blog post for inclusion in a future edition, and volunteer to host the site. You can also check out the Carnival of Mathematics.  Thanks for visiting!

# 2048 Strategy

2048 is a highly popular Math/Puzzle game that can be played on the computer or on mobile devices. The game is about adding two tiles together until you get the number 2048.

The link for the desktop version is: http://gabrielecirulli.github.io/2048/

Like most fun games, the concept of 2048 is deceptively simple, even a 5 year old kid could play it. However, it is hard to master it, and getting the coveted “2048” could prove quite tricky. Do not despair, for after reading this strategy guide, you have a much higher chance of winning the game!

## Strategy Guide / Walkthrough / FAQ

The 3 Top Priorities for 2048 game:

1) Keep your highest tile in the top left corner of the grid. This is your top priority.

2) Do not let low tiles, especially 2’s or 4’s, clog up the upper two rows. This is your second priority.

3) Keep your top row in the following order, from left to right, $2^{n+3}, 2^{n+2}, 2^{n+1}, 2^{n}$. An example would be, 512, 256, 128, 64.

The reason for Priority 1 is that this immensely increases your chances of successful merges of two higher numbers into 1. It synergises with Priority 3 to create a chain-effect. For example, imagine you have 512, 256, 128, 64 on the top row. After merging another 64 with the 64 on the top row, you will have 512, 256, 128, 128. The two 128’s can merge together, making 512, 256, 256. The two 256’s can merge together, making 512, 512. And then, we have a 1024!

The reason for Priority 2 is that letting 2 or 4’s clog up the top rows is very bad. It greatly reduces your mobility (the top 2 rows clogged up with even a single ‘2’ is hard to move). The 2 or 4’s up there have little to no chance to get merged since most of the numbers at the top are high numbers.

Top 3 Guidelines for 2048 game:

1) Press up and left arrows only. Only press right when the upper row is full. Press down only when you have utterly no other choice.

2) Keep the top row filled up, as far as possible.

3) Your general aim is to target the lowest tile on the upper row, to set up the chain effect described above.

Reason for Guideline 1: Pressing right when the upper row is not full has the chance of introducing a new tile on the upper left corner, so now your highest tile is no longer on the upper left corner. This is not good. (Violates Priority 1)

Reason for Guideline 2: Keeping the top row filled up enables you to press “right” without fear of introducing a new tile on the upper left corner.

Reason for Guideline 3: After reaching the late game, we need to think a few steps in advance, and think of which is the best move in accordance to the Top 3 Priorities, and also can target the lowest tile on the upper row to set up a chain effect.

Top 3 Time Saving Quick and Fast Tips for 2048 game

1) The first few steps do not require thinking. Just spam up and left until you get a moderately high number like 128 or 256. There is no harm done about this as the board is uncluttered and there is little chance of losing. You only need to start thinking deeper during the later part of the game, when your highest tile is 512 or more.

2) If Priority 1 is violated, i.e. your highest tile is no longer in the top left corner of the grid, try a few steps to see if you can salvage the situation and get it back to the top left corner. If no, it is better to quit and start a new game to save time. Same for Priority 2, if there is a 2 or 4 clogging the upper row, try a few more steps to see if you can salvage the situation, by merging to make a higher number. If no, we can restart to save time. Priority 3 is less crucial, if the numbers in the top row do not form $2^{n+3}, 2^{n+2}, 2^{n+1}, 2^{n}$, no need to restart. But keep it in mind and keep trying your best to achieve the ideal order.

3) When there is only one possible move, make that move without thinking to save time. (No other choice anyway)

This is the best video on youtube about 2048 Strategy. (Note: They put the highest tile on the bottom right instead. Should be no difference due to the symmetry of the board)

Note: Even the expert maker of this video only has a 30% winning rate! 2048 has some element of luck (the tiles arrive randomly). Personally, I took quite some time to beat the game too.

Good luck! 🙂

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