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Countdown Numbers Game

Tool to solve countdown numbers games automatically. The Numbers Round in the TV Game Show Countdown is a number games which objective is to get a number with the four elementary operators (+, -, ×, ÷) and a list of randomly picked numbers. It is a common exercise/homework for young students.

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Countdown Numbers Game -

Tag(s) : Number Games

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Countdown Numbers Game

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6 Numbers Game Solver (Original)



6 Numbers Game Solver (Improved)


Calculation Mode





Options and Constraints on Operators








Parameters on Calculations








N-Numbers Game Solver



Tool to solve countdown numbers games automatically. The Numbers Round in the TV Game Show Countdown is a number games which objective is to get a number with the four elementary operators (+, -, ×, ÷) and a list of randomly picked numbers. It is a common exercise/homework for young students.

Answers to Questions

How to solve a countdown numbers game?

To find the solutions of a countdown number game, the only method is to make all possible math calculations with the starting tiles (dCode use this method).

The general principle is to start with the list of N numbers, pick 2 and make all operations with these two numbers, if the result is the expected total, note the calculation as possible solution, else, store the result in the list and try again with the N-1 new numbers in the list, and so on.

Example: Numbers 2,6,10, then for each couple among (2,6),(2,10),(6,10), let's take (2,6), make the calculations 2+6=8, 2*6=12, 6-2=4 and 6/2=3 to get 4 new numbers (8,12,4,3) that will make 4 new couples with the remaining 10: (8,10), (12,10), (4,10) and (3,10). Start over with new couples recursively.

Which solver to use?

The original solver uses the rules of the TV Countdown gameshow with 6 number tiles (all natural integers not null), calculations use +, -, *, / operators but avoid non integer divisisions (leading to decimal numbers).

Example: Find 123 with 4,5,6,7,8,9. In 3 operations :
8 + 5 = 13; 13 x 9 = 117; 117 + 6 = 123.

The advanced solver allows more options, constraints on operators, number of operations, etc. It also proposes to generate a list of all possible results from given numbers.

Example: Find 24 by using all numbers 5,5,5,1 and allowing non integers values:
1 / 5 = 0.2; 5 - 0.2 = 4.8; 5 x 4.8 = 24

The N-Numbers solver uses original rules but with any quantity of numbers. Given result is not the easiest one, a random one. Calculation can be very long, billions of iterations, and if there is no answer, it will never end.

What are the most common algorithms for countdown game?

There are three main type of algorithms for solving this number game:

Example: The numbers are 2, 5, 10

Recursive search: make all calculation with N numbers. It uses 2 numbers and for each operation, retry with the results and the N-2 remaining numbers.

Example: Take 2 and 5, make an addition : 2+5=7, a subtraction, 5-2 = 3, etc. Take the result 7 (ou 3), and unused numbers: 10, and start over. 7+10 = 17, etc.

Search with cache: same as the previous one, but stores the calculation to avoid remake them, so, slightly faster, but necessitate a lot of memory.

Example: Take 2 and 5, see if results are already known for addition 7, and subtraction 3, etc. Go on more quickly.

Random search: can find a solution quickly but do not make all calculations, it can prove that a solution exists, but not that a solution does not exist.

Example: Take 2 random numbers 5 and 10, make a random operation : multiplication, store the result : 5*10=50 and go on with remaining results : 2 and 50

How to use negative numbers?

Negative numbers are ignored because they do not influence resolution. Indeed apply the operator - (minus) in front of any negative number to make it positive.

Example: Numbers 3,2,-1 and target 7, calculate 3*2-(-1)=7

Example: Numbers 3,2,1 and target 7, calculate 3*2+=7

What is the distribution of tiles / numbers?

The physical versions of the game have 24 tiles

1 to 102 copies
25, 50, 75 and 1001 copy

How to play Countdown Number Game at school?

The game is ideal for learning how to do calculations in school classes. The board game is available here (link)

Source code

dCode retains ownership of the online 'Countdown Numbers Game' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Countdown Numbers Game download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Countdown Numbers Game tool, so feel free to write! Thank you !


Source : https://www.dcode.fr/countdown-numbers-game
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