The Numbers Game is a great game for those with a mathematical or numerical bent. Each round is quick to play. It can be played by any number of players. Each player also requires a pen and paper.

The game is about taking 6 numbers, and trying to use some or all of these numbers to derive a given target number through the use of standard arithmetic operators: +, -, x and /. So, for example, given the target number of 464, and available numbers: 2, 3, 7, 7, 8, and 9, the objective is to show that these can be used to evaluate to 464, e.g.

7 x 9 = 63
7 x 63 = 441
3 x 8 = 24
441 + 24 - 1 = 464

or, to write it as a formula: (7 x 7 x 9) + ((3 x 8) - 1) = 464

In this case, we've used all the available numbers, but we don't have to use them all each time.

There may be other ways of evaluating 464, but only one is required. Only integer (whole number) results are permissible.

Playing the game

The players first agree how long they should have to try to find a way of making the target number. By default, 30 seconds is allowed, but the players can choose to change this by selecting a different countdown time; the selected countdown time is shown with a green background. They should also agree how many games (or rounds) they will play (or when they will stop playing), and should agree who should select the numbers (generally, players take turns to be the one to choose the six numbers in a series of games).

The player whose turn it is to select the numbers selects six numbers to be displayed, one at a time, by pressing either the Low or High button to select each one. Low numbers are the numbers 1 through to 10, while high numbers are the numbers 25, 50, 75 and 100. Once all six numbers have been selected, a target number is displayed (which will be from 101 through to 999) and the timer starts a countdown.

The players then have to try to find a way of making the target number, or to get as close to this number as possible, from the numbers provided, and write this solution down. No number can be used twice, unless, of course, it appears twice.

When the time is up, the players reveal to each other what number they’ve managed to derive, and how they did it. These can be checked for correctness.

The players who get closest to the target number each receive 5 points. In addition, all players receive bonuses as follows:

  • 10 points if they derive the exact target number;
  • 5 points if they don’t get the exact target number but get a number that is 5 or less away from the target number.

So, if the target number is 729 and there are 5 players (A-E), who achieved the following:

A: 729; B: 733; C: failed to complete correctly; D: 729; E: 723

their scores for the game would be:

A: 5 (closest) + 10 (exact bonus) = 15;
B: 5 (bonus for being within 5 of target);
C: 0;
D: 5 (closest) + 10 (exact bonus) = 15;
E: 0 (not close enough)

Note that even if no player gets within 5 of the goal number, the closest player still gets the score of 5, but no bonuses are scored.

The scores are recorded, and it is then the next player's turn to select the numbers for the next round. The winner of the overall game is, of course, the player with the highest total score.

Starting, Targets and Solutions

When you press the New button to start a new game, or when the app first opens, the target that is displayed after the numbers have been selected is chosen randomly. As soon as the countdown starts, the system starts to calculate as many possible solutions using these numbers as it can, to try to find one that is the target or close to it.

After the countdown stops, or even before this, the Solve button may be tapped. The system then presents a solution (either one that achieves the target, or the nearest it found) in the text area, with the selected numbers used shown in red. Note: pressing the Solve button stops the countdown and the search for solutions.

Alternatively, a new game may be started using the Known button. In this case, the target number presented is one that has a known solution for the numbers given. The way this works is that the system generates many possible solutions that can be derived using the given numbers, and selects one of these as the target number. Tapping the Solve button presents this known solution.

When generating the target number with a known solution, or when searching for solutions to a random target number, the system calculates many possible solutions out of the many more that are possible (the search for solutions is not exhaustive as the number of possible solutions is huge).

This means that the system may not generate a solution that may seem fairly obvious to you, or may miss a solution that uses fewer of the available numbers.

Arithmetic operators to be used

The four operators used are + (addition), - (subtraction), x (multiplication) and / (division), where

9 + 3 = 12
9 - 3 = 6
9 x 3 = 27
9 / 3 = 3


Only whole numbers are allowed in any calculation. So, if the goal number is 130 and the available numbers include 5, 8, 8 and 9, it is not acceptable to use the calculation (9 x 9 x 8) / 5 = 129.6 as being close to 130.

Number distribution

When selecting high and low numbers, the system mimics the idea of having two sets of shuffled card packs, from which it takes the top one whenever a selection is made. You can see how many of each number are available in the table below.



Practising

You can, of course, play the Numbers Game in practice mode by yourself.

Terms of use

This software may be used for personal purposes only.  It may not be used for commercial purposes.

The software, code and script of this application may not be copied or be distributed to others.

The software, code and script may not be altered in any way.

Copyright of the software, code and script, and its help documentation, is held by TopAccolades Limited.  No part of the software, code, script or documentation may be copied or used in another application or document.

Although every effort has been made to ensure that this software functions as intended, TopAccolades Limited provides no warranty of merchantability, or fitness for a particular purpose, in relation to this application or its support.

TopAccolades Limited shall not be liable for any damages whatsoever arising out of the use of or inability to use this application or the provision of or failure to provide support.

Copyright TopAccolades Limited
www.topaccolades.com

Version: 3.0 (20170327)
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