Games 3 page. Scroll down for more games. All games Copyright © 2016-2017
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Space number games. Introductory games of mathematical interest and recreation.
#Four Square #Binary Cube #Eight Square #Trinary Cube #Umbrella #Nine Square #Penta25 #Penta10 #Penta20 #Hexa36 #Hexa30 #Hexa36a #Zerosum4x4 #Bicube
CLICK to play these mathematically beautiful space number games. Copyright © 2016 by Douglas A. Engel, All rights reserved. Scoring, implementation of sound and graphics by Troy Black. Game subject to change at discretion of the authors. Address comments to firstname.lastname@example.org. Copyright © 2016 by Douglas A. Engel
New 4x4 Space Numbers Game. It uses the idea of number as pattern instead of quantity. Each pattern has zero's in the white squares and 2^x in the colored squares. The 4 squares can be thought of as stacked up into one square with the numbers in each stack of 4 squares added together to make the pattern at lower left. You need to move the 4 patterns until you match the lower left number pattern with the number pattern at upper left. Hint: 2^0 pattern shows location of odd numbers, 2^3 pattern shows location of numbers greater than 7. Improves mental, pattern, math, set, intersection, logic.
The Binary Cube game is a 2x2x2 cube Space Number game. This is very easy to solve. Being so small makes it easy to see how the numbers in like positions all add up to produce the counting numbers in the solution and mixed patterns at the left. Eac pattern can be individually rotated about the axis perpendicular to the page. By rotationg and exhanging patterns you can very quickly solve it. The colors help with the solution and noting where the odd numbers must appear in the right hand 2^0 power pattern
New 8x8 Space Numbers game. This can be tricky to solve. You should play the 4x4 game before playing this game. Hint: 2^0 pattern shows location of odd numbers, 2^5 pattern shows location of numbers greater than 31. It is great fun and a little addictive. You could possibly develop an instinct for how the patterns must be positioned.
The Trinary cube is a 3x3x3 Space Numbers game. The rotate button rotates all three power patterns simultaneously about either of two axes making possible rotations of the cube about all three axes. It can take a bit of imagination and logic to solve it. Or you can let the computer solve it by clicking the Solve button.
New Space Numbers game 4x8 "Umbrella". It is like a 4x8 rectangle bent into a circle so that you can rotate the patterns to cause permutation of the colors. It is fun to solve but some of the patterns can be quite tricky.
New 9x9 Trinary Space Numbers game, "Nine Square". You can click on the hints to see solved positions of some of the power patterns. This game uses the base three number system so three number symbols are needed, 0, 1, and 2. Their values are shown as decimal 10 in the small colored squares at the top of the power patterns. It can be solved just by analyzing the numbers in the solved pattern at top right but in some cases it takes more time. The hints are a quick route to a solution. This game will develop your number/pattern senses and the strong symmetries it uses make it very mind expanding.
New Penta25 Space Number game. This game uses the base 5 number system so 5 number/color symbols are needed, 0, 1, 2,3, 4. The pentagram is divided into 25 cells or 5x5 cells. Twenty five is 5^2 but we only need 5^1 and 5^0 to get 0 thru 24 numbers in base 5. The 5^0 symbols are 0, 1, 2,3, 4, and the 5^1 symbols are 0, 5, 10, 15, 20. The game is not difficult and quite fun to master. Usually less than 10 moves required.
New Penta10 Space Number game. This game uses the base 2 number system combined with the base 5 number system so 2 number/color symbols needed are 0,1 abd 5 number/color symbols are needed, 0, 1, 2,3, 4. The pentagram is divided into 10 cells or 2x5 cells. Ten is 5x2 so we only need 5^0 and 2^0 to get 0 thru 9 numbers in base 2;5. The 5^0 symbols are 0, 1, 2,3, 4, and the 2^0 symbols are 0, 1. The game is not difficult and quite fun to master. Usually less than 6 moves required.
New Penta20 game is a 2x2x5 pentagram of 20 cells. This pentagram game is a combine of the 2x5 and 5x5 pentagram games having 2x2x5 = 20 cells. Not hard and lots of fun. Illustrates how space numbers can cooperate or combine.
New Hexa36 Space Number game. Provides democracy among numbers where there is no preferred position or preferred number, number base or place holder. This game uses the base 2 number system combined with the base 3 number system so number/color symbols needed are base two, 0,1 and base three, 0,1,2. The hexagon is divided into 36 cells or 2x2x3x3 cells. We only need 2^0, 2^1 and 3^0, 3^1 power patterns with multipliers to get 0 thru 35 numbers in base 2,3. The game is usually not difficult and quite fun to master just by watching and homing in on the color patterns formed on the solution and mixed patterns. Exchange of columns and rows is allowed so that binary can be primary or trinary can be primary. This is the limited game where pick 2 is not allowed so that only 8 arrangements and two multiplier setups are generated. The unlimited game is more difficult and allows any pick two giving 24 arrangements and 6 multiplier setups.
New Hexa30 Space Number game. This game uses three combined bases, base 2, base 3 and base 5. This may seem preposterous, even ridiculous but it works and it works very well always producing the numbers 0 thru 29. In that sense it is a 30 base, stretching the idea a bit. Two number/color symbols are needed for base two, 0,1 and three for base three, 0,1,2 and five for base five, 0,1,2,3,4. The hexagon is divided into 30 cells or 2x3x5 cells. We only need 2^0, 3^0, 5^0 with multipliers for place holding to get 0 thru 29 numbers. The game is best played by selecting different color display options to give you hints as to the positions of the power patterns. It is not difficult and quite fun to master just by watching and homing in on the color patterns formed on the solution and mixed patterns. The mixing of bases proves that space numbers are a very general mathematical concept.
New Hexa36a advanced Space Number game. This game shows the concept of space numbers can grow in many mind expanding ways. It is advanced by allowing you to pick any two power patterns to exchange. The number formulas adapt for this in six basic ways for all 6! possible binary/trinary pattern mixes. It is a bit harder than Hexa36. As for Hexa36 this game uses the base 2 number system combined with the base 3 number system so number/color symbols needed are base two, 0,1 and base three, 0,1,2. The hexagon is divided into 36 cells or 2x2x3x3 cells. We only need 2^0, 2^1 and 3^0, 3^1 power patterns with multipliers to get 0 thru 35 numbers in base 2,3. The game is quite fun to master just by watching and homing in on the color patterns formed on the solution and mixed patterns. If a certain game looks difficult you can always push the 'pick solution' button to bring up a different game. .
New 4x4 zero sum game. This game uses negative and positive numbers to create a symmetric distribution of negative and positive numbers that always add up to zero. It seems more tricky to solve than 0 thru n space number games.
New 4x2 binary cube game. This one allows the base 4 and base 2 patterns to each be rotated about both x and y axes. With this ability the two cube patterns can be rotated about x, y and z axes by combining different rotations about x and y.
New 4x4x4 bas 4 cube game. You can rotate each cubic power pattern independently. Shows that Space Numbers can be full three dimensional as well as two dimensional. However base 4 was required to achieve the simplest version of thIs game.