2024年美赛MCM/ICM报名正式开启！（附23年美赛O奖C篇优秀论文）

2024年美赛MCM/ICM报名正式开启！

（附23年美赛O奖C篇优秀论文）

1. Multiply the proportions by the number of reports on that day to obtain ” countswith decimal values
2. Round the counts down
3. Add 1 back to the counts. in order from the count which was rounded down most to that which was rounded down least, until the total again matches the number of reports on that day.
This method gives counts which correspond to the given percentages, are integers, and whose sum is the number of reports on that day.
2.2 Wordbank
To model 5-letter words and their properties, we rely on the Stanford GraphBase (SGB) word-bank of 5757 5-letter words created by Donald Knuth 6, which provides a good approximation of the set of words that a player could guess and expect as a target. This word bank is then used in a few different ways. First off, it is used to build the Order Frequency table and the Letter Frequency table. The Letter Frequency table tells us how oftenceach letter appears in 5-letter words, and follows what we would expect. S and E are theanost common letters, followed by A and O. The Order Frequency table then shows given that a certain letter is in the word, what proportion of the time is that letter in each position (e-g. given A is in a word, it is the 4th letter 24% of the time).

namely computing for a given word tthe average number of green, yellow and colored tiles that are returned on any guess chosen uniformly at random from the GB wordbank when t is the actual target word. Additionally, for any word g we compute the average number of colors returned when a target word is chosen uniformly at random from the SGB wordbank and 9 is guessed, which gives a somewhat naive but reasonable metric to evaluate guess words players would use. Using this guess word metric, we compile a list of the 30 words with the highest corresponding average, which we take to be a set of common guess words (see Figure 1) . This list will be used in the calculation of Subset Entropy later on.
As will be detailed later on, we also use this table in numerous word specific calculations.
3 Word Difficulty representation
Many factors contribute towards the difficulty associated with a given word. For example.zingy intuitively seems to be difficult for a variety of reasons – it has uncommon letters (“z”and“y”),only one “canonical ”vowel ,and is a generally infrequently used word in English.A word like onion’ on the other hand would also seem to be difficult, despite all of its letters being fairly common and its usage in every day spoken language being much higher. The reason it is perceived as difficult is due to a repetition of the letter ” o and n, which people may be less likely to guess again once they have already discovered one position of. Thus, given a word, our first task was to list and quantify such characteristics, so that when evaluating word difficulty later on we could instead simply oonsider the vector of values corresponding to these relevant characteristics.