2023年美國大學生數學建模競賽（MCM/ICM）C題賽題公布

Category: 數模國際競賽 Date: 2023年2月17日下午5:56

萬眾矚目的2023年度美賽終于正式開賽了！2023年美賽已于北京時間2月17日6:00正式開賽。為了幫大家節省時間和精力，小編為大家帶來了今年美賽的題目以及中文翻譯！翻譯結果可能存在一定誤差，僅供參考，請各參賽隊伍結合原文進行理解作答！

預祝各位參賽的同學都能獲得理想的成績！

C題：大數據

Problem C: Predicting Wordle Results

Background

Wordle is a popular puzzle currently offered daily by the New York Times. Players try to solve the puzzle by guessing a five-letter word in six tries or less, receiving feedback with every guess. For this version, each guess must be an actual word in English. Guesses that are not recognized as words by the contest are not allowed. Wordle continues to grow in popularity and versions of the game are now available in over 60 languages.

The New York Times website directions for Wordle state that the color of the tiles will change after you submit your word. A yellow tile indicates the letter in that tile is in the word, but it is in the wrong location. A green tile indicates that the letter in that tile is in the word and is in the correct location. A gray tile indicates that the letter in that tile is not included in the word at all (see Attachment 2)[2]. Figure 1 is an example solution where the correct result was found in three tries.

圖 1: 2022年7月21日單詞拼圖的示例解決方案[3]

Players can play in regular mode or “Hard Mode.” Wordle’s Hard Mode makes the game more difficult by requiring that once a player has found a correct letter in a word (the tile is yellow or green), those letters must be used in subsequent guesses. The example in Figure 1 was played in Hard Mode.

Many (but not all) users report their scores on Twitter. For this problem, MCM has generated a file of daily results for January 7, 2022 through December 31, 2022 (see Attachment 1). This file includes the date, contest number, word of the day, the number of people reporting scores that day, the number of players on hard mode, and the percentage that guessed the word in one try, two tries, three tries, four tries, five tries, six tries, or could not solve the puzzle (indicated by X). For example, in Figure 2 the word on July 20, 2022 was “TRITE” and the results were obtained by mining Twitter. Although the percentages in Figure 2 sum to 100%, in some cases this may not be true due to rounding.

圖2:2022年7月20日報告結果在Twitter上的分布[4]

Requirement

You have been asked by the New York Times to do an analysis of the results in this file to answer several questions.

The number of reported results vary daily. Develop a model to explain this variation and use your model to create a prediction interval for the number of reported results on March 1, 2023. Do any attributes of the word affect the percentage of scores reported that were played in Hard Mode? If so, how? If not, why not?

For a given future solution word on a future date, develop a model that allows you to predict the distribution of the reported results. In other words, to predict the associated percentages of (1, 2, 3, 4, 5, 6, X) for a future date. What uncertainties are associated with your model and predictions? Give a specific example of your prediction for the word EERIE on March 1, 2023. How confident are you in your model’s prediction?

Develop and summarize a model to classify solution words by difficulty. Identify the attributes of a given word that are associated with each classification. Using your model, how difficult is the word EERIE? Discuss the accuracy of your classification model.

List and describe some other interesting features of this data set.

Finally, summarize your results in a one- to two-page letter to the Puzzle Editor of the New York Times.

Your PDF solution of no more than 25 total pages should include:

One-page Summary Sheet.

Table of Contents.

Your complete solution.

One- to two-page letter.

Reference List.

Note: The MCM Contest has a 25-page limit. All aspects of your submission count toward the 25-page limit (Summary Sheet, Table of Contents, Report, Reference List, and any Appendices). You must cite the sources for your ideas, images, and any other materials used in your report.

Attachments

1.Data File. Problem C Data Wordle.xlsx

THE ATTACHED DATA FILE CONTAINS THE ONLY DATA YOU SHOULD USE FOR THIS PROBLEM. All information needed for this problem is given in the problem statement and the data file. You do not need to visit the New York Times website nor Twitter website. There is no additional information to be found on these sites.

Data File Entry Descriptions

Date: The date in mm-dd-yyyy (month-day-year) format of a given Wordle puzzle.

Contest number: An index of the Wordle puzzles, beginning with 202 on January 7, 2022.

Word: The solution word players are trying to guess on the associated date and contest number.

Number of reported results: The total number scores that were recorded on Twitter that day.

Number in hard mode: The number of scores on Hard mode recorded on Twitter that day.

1 try: The percentage of players solving the puzzle in one guess.

2 tries: The percentage of players solving the puzzle in two guesses.

3 tries: The percentage of players solving the puzzle in three guesses.

4 tries: The percentage of players solving the puzzle in four guesses.

5 tries: The percentage of players solving the puzzle in five guesses.

6 tries: The percentage of players solving the puzzle in six guesses.

7 or more tries (X): The percentage of players that could not solve the puzzle in six or fewer tries. Note: the percentages may not always sum to 100% due to rounding.

2.Directions of Wordle posted to the New York Times website.[2]

Glossary

New York Times: A daily newspaper based in New York City, New York, USA published in print and online.

Twitter: A social networking site that allows users to broadcast short posts of no more than 280 characters (increased from initial 140 characters).

Solve (the Wordle puzzle): Enter the correct letters in the correct order to form the Wordle word of the day.

References

Note: We provide the following citations to support the Problem Statement. We have pulled the important ideas from these resources. There is no additional information on these websites needed to solve this MCM problem. Access to the New York Times or Twitter website is not required to solve this problem.

[1] Wordle logo from The New York Times website. Accessed on December 13, 2022 at https://nytco-assets.nytimes.com/2022/08/cropped-Screen-Shot-2022-08-24-at-8.49.39-AM.png.

[2] “Wordle-The New York Times.” The New York Times, 2022. Accessed December 13, 2022 at https://www.nytimes.com/games/wordle/index.html.

[3] “Wordle-The New York Times.” The New York Times, July 21, 2022.

[4] “Wordle Stats.” Twitter, July 20, 2022.

中文賽題 C：預測Wordle結果

背景

Wordle是由《紐約時報》每天推出的一種受歡迎的益智游戲。玩家們需要在六次或更少的猜測中猜出一個由五個字母組成的單詞，并在每次猜測后得到反饋。在這個版本中，每個猜測必須是英語中的一個實際單詞。比賽中不被認可為單詞的猜測是不允許的。Wordle在人們中不斷增長的流行度中，現在有60多種語言的游戲版本可供選擇。

《紐約時報》網站上關于Wordle的說明指出，在提交單詞后，瓷磚的顏色會發生變化。黃色的瓷磚表示該瓷磚中的字母在單詞中，但位置不正確。綠色的瓷磚表示該瓷磚中的字母在單詞中，位置正確。灰色的瓷磚表示該瓷磚中的字母根本不包含在單詞中（見附件2）。圖1是一個示例解決方案，其中在三次嘗試中找到了正確答案。

Figure 1: Example Solution of Wordle Puzzle from July 21, 2022[3]

玩家可以在常規模式或“困難模式”下玩。Wordle的困難模式通過要求一旦玩家在單詞中找到正確的字母（瓷磚為黃色或綠色），就必須在隨后的猜測中使用這些字母來使游戲更加困難。圖1中的示例是在困難模式下玩的。

許多（但并非所有）用戶會在Twitter上報告他們的得分。對于這個問題，MCM已經生成了一個文件，記錄了2022年1月7日至2022年12月31日的每日結果（見附件1）。該文件包括日期、比賽編號、當天的單詞、當天報告得分的人數、在困難模式下的玩家人數，以及猜出單詞的百分比，包括一次、兩次、三次、四次、五次、六次或無法解決的謎題（表示為X）。例如，圖2中的單詞是“TRITE”，日期是2022年7月20日，結果是通過在Twitter上收集得到的。盡管圖2中的百分比總和為100%，但在某些情況下，由于四舍五入，這可能不是真實的。

Figure 2: Distribution of the Reported Results for July 20, 2022 to Twitter[4]

要求

紐約時報要求您對該文件中的結果進行分析，以回答幾個問題。

報告的結果數量每天都有所不同。開發一個模型來解釋這種變化，并使用您的模型創建一個關于2023年3月1日報告結果數量的預測區間。是否有單詞的屬性會影響報告的得分中在困難模式下玩的比例？如果有，是怎樣的？如果沒有，為什么？

對于未來日期的給定解決方案單詞，開發一個模型，使您可以預測報告結果的分布。換句話說，預測未來日期的相關百分比（1、2、3、4、5、6、X）的分布。您的模型和預測有哪些不確定性？請舉一個關于2023年3月1日單詞EERIE的預測的具體例子。您對您模型的預測有多自信？

開發并總結一個模型，通過難度分類解決方案單詞。確定與每個分類相關聯的給定單詞的屬性。使用您的模型，單詞EERIE有多難？討論您的分類模型的準確性。

列出并描述該數據集的其他有趣特征。

最后，用一頁至兩頁的信函，對紐約時報的謎題編輯總結您的結果。

您的PDF解決方案總頁數不超過25頁，其中包括：

一頁摘要。

目錄表。

您的完整解決方案。

一頁至兩頁的信函。

參考文獻列表。

注意：MCM學術活動有25頁的限制。您的所有提交內容都計入25頁限制（總結表、目錄表、報告、參考文獻列表以及任何附錄）。您必須引用您報告中使用的想法、圖片和其他材料的來源。

術語表

紐約時報：一份總部位于美國紐約市的日報，以印刷和在線出版為主。Twitter：一種社交網絡網站，允許用戶發布不超過 280 個字符的短消息（最初是 140 個字符）。解決（Wordle 拼圖）：按正確的順序輸入正確的字母以形成當天的 Wordle 單詞。

參考資料

注：我們提供以下引文以支持問題陳述。我們從這些資源中提取了重要的想法。這些網站上沒有解決MCM問題所需的其他信息。解決這個 MCM 問題不需要訪問紐約時報或 Twitter 網站。

[1] Wordle logo from The New York Times website. Accessed on December 13, 2022 at https://nytco-assets.nytimes.com/2022/08/cropped-Screen-Shot-2022-08-24-at-8.49.39-AM.png.

[2] “Wordle-The New York Times.” The New York Times, 2022. Accessed December 13, 2022 at https://www.nytimes.com/games/wordle/index.html.

[3] “Wordle-The New York Times.” The New York Times, July 21, 2022.

[4] “Wordle Stats.” Twitter, July 20, 2022.

這里為了讓大家對今年的美賽有一個直接客觀的了解。對2023年美賽(MCM/ICM)進行一下簡要的介紹。

一、學術活動時間

February 16-20, 2023

開賽時間北京時間 17號(本周五) 6:00

結束時間?北京時間?21號(下周二) 9:00

提交截止時間? ? ? ? ??21號(下周二) 10:00

比賽結果 ??? ? ? ? ? ? ? ?5月30號之前公布

2023 Contest Dates and Times:

Registration Deadline: Before 3:00 p.m. EST on Thursday, February 16, 2023.

Contest Starts: 5:00 p.m. EST on Thursday, February 16, 2023.

Contest Ends: 8:00 p.m. EST on Monday, February 20, 2023.

Solution Report Deadline: 9:00 p.m. EST on Monday, February 20, 2023.

Contest Results: The results will be posted on or before May 31, 2023.

二、2023年美賽變化

在推特上關注@COMAPMath或在微博上關注COMAPCHINAOFFICIAL，以獲取最新信息。

注冊流程已簡化，分為兩部分：顧問注冊和團隊注冊。

MCM/ICM學術活動現在有25頁的限制。25 頁的限制適用于整個提交，包括摘要表、解決方案、參考列表、目錄、注釋、附錄、代碼和任何問題特定要求。

由于 Covid-19 病毒，鼓勵團隊使用電子通信進行虛擬會議。但是，您的團隊成員只能與自己團隊的成員進行交流。規則仍然是，團隊不得使用除自己的團隊成員以外的任何人來討論或獲取處理和解決問題的想法。

Follow @COMAPMath on Twitter or COMAPCHINAOFFICIAL on Weibo for the most up to date information.

Registration process has been streamlined and split into 2 parts: Advisor Registration and Team Registration.

The MCM/ICM Contest now have a 25 page limit. The 25 page limit applies to the entire submission including the Summary Sheet, Solution, Reference List, Table of Contents, Notes, Appendices, Code and any problem specific requirements.

Due to the Covid-19 virus teams are encouraged to meet virtually using electronic communications. BUT, your team members may only communicate with members of their own team. The rule remains that teams may not use any persons, other than their own team members, to discuss or obtain ideas for working on and solving their problem.

三、賽題基本情況

美賽目前分為兩種類型，MCM（Mathematical Contest In Modeling）和ICM（Interdisciplinary Contest In Modeling)，兩種類型學術活動采用統一標準進行，學術活動題目出來之后，參賽隊伍通過美賽官網進行選題，一共分為下面6種題型。

MCM

A 連續型

B 離散型

C 大數據

ICM

D 運籌學/圖與網絡

E?環境可持續

F 政策

題目分類大致如此，但是近年來題目也開始發生微小變化，例如E題，之前都是環境相關的題目，今年開始與可持續性聯系尤為緊密。

MCM:全稱The Mathematical Contest in Modeling，即數學建模學術活動，偏自然、理工科。對于參賽者的數學模型素養以及建模能力要求較高，