# Guess the Numbers: A Fun and Challenging Math Game for All Ages

In this game, players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player(s) who select a number closest to 2/3 of the average of numbers chosen by all players.[2]

## guess the numbers

Alain Ledoux is the founding father of the guess 2/3 of the average-game. In 1981, Ledoux used this game as a tie breaker in his French magazine Jeux et StratÃ©gie. He asked about 4,000 readers, who reached the same number of points in previous puzzles, to state an integer between 1 and 1,000,000,000. The winner was the one who guessed closest to 2/3 of the average guess.[3] Rosemarie Nagel (1995) revealed the potential of guessing games of that kind: They are able to disclose participants' "depth of reasoning."[4]

Due to the analogy to Keynes's comparison of newspaper beauty contests and stock market investments[6] the guessing game is also known as the Keynesian beauty contest.[7] Rosemarie Nagel's experimental beauty contest became a famous game in experimental economics. The forgotten inventor of this game was unearthed in 2009 during an online beauty contest experiment with chess players provided by the University of Kassel:[8] Alain Ledoux, together with over 6,000 other chess players, participated in that experiment which looked familiar to him.[9][10]

Intuitively, guessing any number higher than 2/3 of what you expect others to guess on average cannot be part of a Nash equilibrium. The highest possible average that would occur if everyone guessed 100 is 66+2/3. Therefore, choosing a number that lies above 66+2/3 is strictly dominated for every player. These guesses can thus be eliminated. Once these strategies are eliminated for every player, 66+2/3 becomes the new highest possible average (that is, if everyone chooses 66+2/3). Therefore, any guess above 44+4/9 is weakly dominated for every player since no player will guess above 66+2/3, and 2/3 of 66+2/3 is 44+4/9. This process will continue as this logic is continually applied, If the same group of people play the game consistently, with each step, the highest possible logical answer keeps getting smaller, the average will move close to 0, all other numbers above 0 have been eliminated. If all players understand this logic and select 0, the game reaches its Nash equilibrium, which also happens to be the Pareto optimal solution.[11] At this state, every player has chosen to play the best response strategy for themselves, given what everyone else is choosing.

This game illustrates the difference between the perfect rationality of an actor and the common knowledge of the rationality of all players. To achieve its Nash equilibrium of 0, this game requires all players to be perfectly rational, rationality to be common knowledge, and all players to expect everyone else to behave accordingly.[12] Common knowledge means that every player has the same information, and they also know that everyone else knows that, and that everyone else knows that everyone else knows that, and so on, infinitely.[13] Common knowledge of rationality of all players is the reason why the winning guess is 0.

Economic game theorists have modelled this relationship between rationality and the common knowledge of rationality through K-level reasoning. K stands for the number of times a cycle of reasoning is repeated. A Level-k model usually assumes that k-level 0 agents would approach the game naively and make choices distributed uniformly over the range [0, 100]. In accordance with cognitive hierarchy theory, level 1 players select the best responses to level 0 choices, while level 2 players select the best responses to level 1 choices.[14] Level 1 players would assume that everyone else was playing at level 0, responding to an assumed average of 50 in relation to naive play, and thus their guess would be 33 (2/3 of 50). At k-level 2, a player would play more sophisticatedly and assume that all other players are playing at k-level 1, so they would choose 22 (2/3 of 33).[15] Players are presumptively aware of the probability distributions of selections at each higher level. It would take approximately 21 k-levels to reach 0, the Nash equilibrium of the game.

The guessing game depends on three elements: (1) the subject's perceptions of the level 0 would play; (2) the subject's expectations about the cognitive level of other players; and (3) the number of in-game reasoning steps that the subject is capable of completing.[16] Evidence suggest that most people play at k-levels 0 to 3,[17] so you would just have to think one step ahead of that to have a higher chance at winning the game. Therefore, being aware of this logic allow players to adjust their strategy. This means that perfectly rational players playing in such a game should not guess 0 unless they know that the other players are rational as well, and that all players' rationality is common knowledge. If a rational player reasonably believes that other players will not follow the chain of elimination described above, it would be rational for him/her to guess a number above 0 as their best response.

In reality, we can assume that most players are not perfectly rational, and do not have common knowledge of each other's rationality.[18] As a result, they will also expect others to have a bounded rationality and thus guess a number higher than 0.

Experiments demonstrate that many people make mistakes and do not assume common knowledge of rationality. It has been demonstrated that even economics graduate students do not guess 0.[4] When performed among ordinary people it is usually found that the winner's guess is much higher than 0: the winning value was found to be 21.6 in a large online competition organized by the Danish newspaper Politiken. 19,196 people participated and the prize was 5000 Danish kroner.[19]

Returns the internal rate of return for a series of cash flows represented by the numbers in values. These cash flows do not have to be even, as they would be for an annuity. However, the cash flows must occur at regular intervals, such as monthly or annually. The internal rate of return is the interest rate received for an investment consisting of payments (negative values) and income (positive values) that occur at regular periods.

guess the number game online

guess the number math is fun

guess the number activity for kids

guess the number python code

guess the number challenge with friends

guess the number between 1 and 100

guess the number using binary search

guess the number with clues and hints

guess the number word problems

guess the number app for android

guess the number in as few tries as possible

guess the number abcya educational game

guess the number interactive whiteboard

guess the number java program

guess the number logic puzzle

guess the number worksheet pdf

guess the number funbrain arcade game

guess the number javascript tutorial

guess the number mental math skills

guess the number smartboard lesson

guess the number c++ project

guess the number bingo cards

guess the number cool math games

guess the number python 3

guess the number scratch game

guess the number using algebra

guess the number flashcards quizlet

guess the number khan academy video

guess the number powerpoint presentation

guess the number random generator

guess the number riddle me this

guess the number board game rules

guess the number excel spreadsheet

guess the number google classroom assignment

guess the number ixl learning module

guess the number javascript codepen

guess the number math playground game

guess the number printable worksheets

guess the number python repl.it

guess the number quiz for kids

guess the number ruby script

guess the number stem activity

guess the number trivia questions

guess the number using fractions

guess the number visual basic code

guess the number with emojis and symbols

guess the number youtube video

how to play guess the number game

Microsoft Excel uses an iterative technique for calculating IRR. Starting with guess, IRR cycles through the calculation until the result is accurate within 0.00001 percent. If IRR can't find a result that works after 20 tries, the #NUM! error value is returned.

At the same time, the mentalist quickly writes down the numbers with a Swami pencil. This is a piece of plastic with lead at the end attached to the mentalists, say, thumb. (Refer to picture above.)

The mentalist actually planted a set of numbers on the notepad before asking the volunteers to write down their numbers. He then strategically hands the notepad with the empty side facing up as the volunteers write their numbers.

Write a program that prints to the user the sum (a+b) and product (a*b) of two randomly generated natural numbers (positive integers) between 1 and 100. To win the game the user must guess the two numbers, the order of the guess should not matter. The user is given three guesses, if they are wrong after three guesses then the numbers are revealed to them. The user has to guess both guesses correctly in a single round and is not told if one of the numbers in a previous round was correct.The user has 3 attempts to guess the two numbers, and the game should finish if the user guesses the numbers correctly.

We were given a homework assignment to create a C++ program that generates 3 different random numbers each time and the user is supposed to guess the three of them AND in order. I already achieved that, however I'm not very satisfied with how long my code is, especially with the fact that I had so many if statements. We were told at the beginning of the year that good programming is the ability to write less but more efficiently.(We haven't learned anything about arrays or vectors yet) but I'm still curious to know what are other ways to compare the 3 generated numbers and the 3 user input numbers, all while keeping the order criterion in mind)

PS. 3 guesses of 3 numbers in order -> User wins. If the users fails to guess the 3 numbers in their order within 10 attempts, they lose + I also kept the generated numbers to print out just for testing purposes.ALSO, we were required to have 3 functions so that's why I didn't write everything in just one.

Here is an example routine to count a number of numbers appearing in two sets, implemented as vectors of ints. Please note the routine takes data by value (i.e. a copy) so that it can modify (sort) them without affecting the caller's data.

At a given draw you are choosing one of $49\choose3=18424$ triples at random. Since $6$ numbers will be drawn there are $6\choose3=20$ successful triples. It follows that the probability $p$ of a success in one draw is given by$$p=20\over18424\doteq0.00108554\ .$$The probability $q$ that you fail in all of 1248 draws is therefore given by$$q=(1-p)^1248\doteq0.25782\ .$$Therefore you can count on succeeding at least once in two years with probability $1-q\doteq0.74218$.

Assuming numbers can be repeated, this gives a result of about $1.2$, which means you can be pretty sure of winning once in $2$ years. $576$ times profit is still an inadequate amount for $1248$ tries, but its worth trying your luck.

Time Complexity: The time complexity of this code is O(n) as the number of iterations of the loop is not fixed and depends on the number of guesses taken by the user to get the right answer.

Basically, in the Powerball, there are two drums that have numbered balls in them. Then, the balls are drawn publicly, one at a time. The goal is to guess which randomly selected numbers will get drawn.

If you have a Powerball ticket that matches all of the winning numbers pulled out from the first drum and matches the Powerball that is pulled out of the second drum, you win the jackpot! If you only have some of the winning numbers, you can still win a generous amount of money, anywhere between $4 and $1 million.