Table of results for double numbers:
What I notice:
I notice that the Maxi product is retrieved when the two halves of the selected number are multiplied together. I also notice that the two halves are always the same.
For example, 12; twelve will have a Maxi Product of 36 as the half of twelve is six and six multiplied by itself will give you 36 which is the Maxi Product of 12.
Testing my Theory
The maximum product that can be retrieved by the number 8 is 16. You get this by halving 8, which is 4 and then multiplying by itself, which gives you, 16. I will test this now.
(1,7)= 8 → 1+7 → 1x7=7
(2,6)= 8 → 2+6 → 2x6=12
(3,5)= 8 → 3+5 → 3x5=15
(4,4)= 8 → 4+4 → 4x4=16
I have found that 16 is the highest number so far that can be retrieved from 4 and 4 when the number is 8, in whole numbers. I will now try in decimal numbers if I can get a number higher than 16.
(4.7,3.3)= 8 → 4.7+3.3 → 4.7x3.3=15.51
(4.1,3.9)= 8 → 4.1+3.9 → 4.1x3.9=15.99
I still have not yet found a number higher than 16 in decimal numbers. I will try now in fractional numbers if I can get a number higher than 16.
(4 1/20, 3 19/20) =8 → 4 1/20+3 19/20 → 4 1/20x3 19/20 =15.9975
(4 1/50, 3 49/50) =8 → 4 1/50+3 49/50 → 4 1/20x3 49/50 =15.996
(4 1/100, 3 99/100)=8 → 4 1/100+3 99/100 → 4 1/100x3 99/100= 15.9999
I have found that 16 is the Maxi Product of 8 as the two numbers, 4 and 4, when multiplied together make 16. So, my theory was right.
Rule in Words:
Maxi Product equals the number selected divided by two and then the answer squared.
Rule in Algebra:
M=(N/2)²
Key:
M= Maxi Product
N= Number that has been selected
Proving my rule:
Find the Maxi Product of a) 44 b) 55 and c) 66.
A) M=(N/2)² B) M=(N/2)² C) M=(N/2)²
M=(44/2)² M=(55/2)² M=(66/2)²
M=484 M=756.25 M=1089
Triple Numbers
Examples:12
(1,9,2)= 12 → 1+9+2 → 1x9x2=18
(2,8,2)= 12 → 2+8+2 → 2x8x2=32
(3,7,2)= 12 → 3+7+2 → 3x7x2=42
(3,6,3)= 12 → 3+6+3 → 3x6x3=54
(4,5,3)= 12 → 4+5+3 → 4x5x3=60
(4,4,4)= 12 → 4+4+4 → 4x4x4=64
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 64 when three numbers are multiplied together.
(4,4.1,3.9)= 12 → 4+4.1+3.9 → 4x4.1x3.9 =63.96
(4,4.2,3.8)= 12 → 4+4.2+3.8 → 4x4.2x3.8 =63.84
(4.2,3.9,3.9)= 12 → 4.2+3.9+3.9 → 4.2x3.9x3.9=63.882
I am now going to use fractional numbers as I yet have not found a number that is the product of three numbers that leaves a result that is more than 64. I will see in fractional number if I can retrieve a number higher than 64 by multiplying three numbers together.
(4 1/10,4 4/10,3 5/10)= 12 → 4 1/10+4 4/10+3 5/10 → 4 1/10x4 4/10x3 5/10 = 63.14
(4 1/15,4 11/15,3 3/15)= 12 → 4 1/15+4 11/15+3 3/15 → 4 1/15x4 11/15x3 3/15=61.596
(3dp)
(4 1/3,4 1/3,3 1/3)= 12 → 4 1/3+4 1/3+3 1/3 → 4 1/3x4 1/3x3 1/3 =62.59
(2dp)
I have found that 4, 4, and 4 are the three numbers which added together make 12 and when multiplied together make 64 which is the highest possible answer which can be retrieved when three numbers added together equal 12 are multiplied.
13
(1,11,1)= 13 → 1+11+1 → 1x11x1=11
(2,10,1)= 13 → 2+10+1 → 2x10x1=20
(2,9,2)= 13 → 2+9+2 → 2x9x2 =36
(3,8,2)= 13 → 3+8+2 → 3x8x2 =48
(3,7,3)= 13 → 3+7+3 → 3x7x3 =63
(4,6,3)= 13 → 4+6+3 → 4x6x3 =72
(4,5,4)= 13 → 4+5+4 → 4x5x4 =80
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 80 when three numbers are multiplied together.
(4.1,4.8,4.1)= 13 → 4.1+4.8+4.1 → 4.1x4.8x4.1=80.688
(4.2,4.6,4.2)= 13 → 4.2+4.6+4.2 → 4.2x4.6x4.2=81.144
(4.3,4.4,4.3)= 13 → 4.3+4.4+4.3 → 4.3x4.4x4.3=81.356
I will now move onto fractional numbers as there can be no other decimal number that can give a result higher than 81.356 using three numbers. I will see in fractional numbers if I can get a number higher than 81.356 from three fractional numbers.
(4 1/2 ,4 1/4,4 1/4)= 13 → 4 1/2+4 1/4+4 1/2 → 4 1/2x4/14x4 1/4 =81.28125
(4 5/16,4 5/16, 4 6/16)= 13 → 4 5/16+4 5/16+4 6/16 → 4 5/16x4 5/16x 4 6/16=81.364
(3dp)
(4 1/3,4 1/3,4 1/3)= 13 → 4 1/3+4 1/3+4 1/3 → 4 1/3x4 1/3x4 1/3 =81.370
(3dp)
I have found that 4 1/3, 4 1/3, and 4 1/3 are the three numbers which added together make 13 and when multiplied together make 81.370 (3dp) which is the highest possible answer which can be retrieved when three numbers added together equal 13 are multiplied.
14
(1,12,1)= 14 → 1+12+1 → 1x12x1=12
(2,11,1)= 14 → 2+11+1 → 2x11x1=22
(2,10,2)= 14 → 2+10+2 → 2x10x2=40
(3,9,2)= 14 → 3+9+2 → 3x9x2 =54
(3,8,3)= 14 → 3+8+3 → 3x8x3 =72
(4,7,3)= 14 → 4+7+3 → 4x7x3 =84
(4,6,4)= 14 → 4+6+4 → 4x6x4 =96
(5,5,4)= 14 → 5+5+4 → 5x5x4 =100
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 100 when three numbers are multiplied together.
(4.7,4.9,4.4)= 14 → 4.7+4.9+4.4 → 4.7x4.9x4.4=101.332
(4.7,4.7,4.6)= 14 → 4.7+4.7+4.6 → 4.7x4.7x4.6=101.614
I will now move on to fractional numbers as there can be no other decimal number that can give a result higher than 101.614 using three numbers. I will see in fractional numbers if I can get a number higher than 101.332 from three fractional numbers.
(5 1/3,4 1/3,4 1/3)= 14 → 5 1/3+4 1/3+4 1/3 → 5 1/3x4 1/3x4 1/3= 100.148 (3dp)
(4 2/3,4 2/3,4 2/3)= 14 → 4 2/3+4 2/3+4 2/3 → 4 2/3x4 2/3x4 2/3= 101.6296296
I have found that 4 2/3, 4 2/3, and 4 2/3 are the three numbers which added together make 14 and when multiplied together make 101.6296296 which is the highest possible answer which can be retrieved when three numbers added together equal 14 are multiplied.
15
(1,13,1)= 15 → 1+13+1 → 1x13x1=13
(2,12,1)= 15 → 2+12+1 → 2x12x1=24
(2,11,2)= 15 → 2+11+2 → 2x11x2=44
(3,10,2)= 15 → 3+10+2 → 3x10x2=60
(3,9,3)= 15 → 3+9+3 → 3x9x3 =81
(4,8,3)= 15 → 4+8+3 → 4x8x3 =96
(4,7,4)= 15 → 4+7+4 → 4x7x4 =112
(5,6,4)= 15 → 5+6+4 → 5x6x4 =120
(5,5,5)= 15 → 5+5+5 → 5x5x5 =125
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 125 when three numbers are multiplied together.
(5.1,4.8,5.1)= 15 → 5.1+4.8+5.1 → 5.1x4.8x5.1=124.848
(5.3,4.4,5.3)= 15 → 5.3+4.4+5.3 → 5.3x4.4x5.3=123.596
I will now move on to fractional numbers as there is no decimal number that can give a result higher than 125 using three numbers. I will see in fractional numbers if I can get a number higher than 125 from three fractional numbers.
(5 1/80,5 70/80,4 9/80)= 15 → 5 1/80+5 70/80+4 9/80 → 5 1/80x5 70/90x4 9/80=121.11
(2dp)
(5 5/90,5 80/90,4 5/90)= 15 → 5 5/90+5 80/90+4 5/90 → 5 5/90x5 80/90x4 5/90=120.74
(2dp)
I have found that 5, 5, and 5 are the three numbers which added together make 15 and when multiplied together make 125 which is the highest possible answer which can be retrieved when three numbers added together equal 15 are multiplied.
16
(1,14,1)= 16 → 1+14+1 → 1x14x1=14
(2,13,1)= 16 → 2+13+1 → 2x13x1=26
(2,12,2)= 16 → 2+12+2 → 2x12x2=48
(3,11,2)= 16 → 3+11+2 → 3x11x2=66
(3,10,3)= 16 → 3+10+3 → 3x10x3=90
(4,9,3)= 16 → 4+9+3 → 4x9x3 =108
(4,8,4)= 16 → 4+8+4 → 4x8x4 =128
(5,7,4)= 16 → 5+7+4 → 5x7x4 =140
(5,6,5)= 16 → 5+6+5 → 5+6+5 =150
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 150 when three numbers are multiplied together.
(5.01,5.90,5.09)= 16 → 5.01+5.90+5.09 → 5.01x5.90x5.09=150.45531
(5.25,5.30,5.45)= 16 → 5.25+5.30+5.45 → 5.25x5.30x5.45=151.64625
I will now move on to fractional numbers as there can be no other decimal number that can give a result higher than 151.64625 using three numbers. I will see in fractional numbers if I can get a number higher than 151.64625 from three fractional numbers.
(5 1/20,5 7/20,5 12/20)= 16 → 5 1/20+5 7/20+5 12/20 → 5 1/20x5 7/20x5 12/20=
151.298
(5 1/50,5 20/50,5 29/50)= 16 → 5 1/50+5 20/50+5 29/50 → 5 1/50x5 20/50x5 29/50=
151.26264
(5 1/3,5 1/3,5 1/3)= 16 → 5 1/3+5 1/3+5 1/3 → 5 1/3x5 1/3x5 1/3=151.704
(3dp)
I have found that 5 1/3, 5 1/3, and 5 1/3 are the three numbers which added together make 16 and when multiplied together make 151.704 (3dp) which is the highest possible answer which can be retrieved when three numbers added together equal 16 are multiplied.
Result of Numbers:
Table of results for triple numbers:
What I Notice:
I notice that the Maxi Product is retrieved when the number is split up into three parts and then multiplied together.
For example, 12, twelve will have a Maxi Product of 64 as a third of 12 is 4, and 4 multiplied by itself three times gives you 64. I will now test my theory.
Testing my theory:
The maximum product that can be retrieved by 8 is 18.963 (3dp). You get this by finding one third of 8 and then multiplying it by itself three times, which is 18.963 (3dp). I will prove this now.
(1,6,1)= 8 → 1+6+1 → 1x6x1=6
(2,5,1)= 8 → 2+5+1 → 2x5x1=10
(2,4,2)= 8 → 2+4+2 → 2x4x2=16
(3,3,2)= 8 → 3+3+2 → 3x3x2=18
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 18 when three numbers are multiplied together.
(3.2,2.6,2.2)= 8 → 3.2+2.6+2.2 → 3.2x2.6x2.2=18.304
(3.6,3.6,0.8)= 8 → 3.6+3.6+0.8 → 3.6x3.6x0.8=10.368
(3.1,2.8,2.1)= 8 → 3.1+2.8+2.1 → 3.1x2.8x2.1=18.228
(2.6,2.6,2.8)= 8 → 2.6+2.6+2.8 → 2.6x2.6x2.8=18.928
I will now move onto fractional numbers as there can be no other decimal number that can give a result higher than 18.928 using three numbers. I will see in fractional numbers if I can get a number higher than 18.928 from three fractional numbers.
(2 1/3,2 1/3,3 1/3)= 8 → 2 1/3+2 1/3+3 1/3 → 2 1/3x2 1/3x3 1/3=18.148 (3dp)
(2 2/3,2 2/3,2 2/3)= 8 → 2 2/3+2 2/3+2 2/3 → 2 2/3x2 2/3x2 2/3=18.963 (3dp)
I have found that 2 2/3,2 2/3 and 2 2/3 are the three numbers which added together make 8 and when multiplied together make 18.963 (3dp) which is the highest possible answer which can be retrieved when three numbers added together equal 8 are multiplied.
Rule in words:
Maxi Product equals the number divided by three and then the answer cubed.
Rule in Algebra:
M=(N/3)³
Key:
M=Maxi product
N=Number that is highlighted
Proving my rule:
Find the Maxi Product of a)44 b)55 and c)66
a) M=(N/3)³ b) M=(N/3)³ c) M=(N/3)³
M=(44/3)³ M=(55/3)³ M=(55/3)³
M=3154.963 (3dp) M=6162.037 M=10648
Quadruplet Numbers:
12
(1,1,1,9)= 12 → 1+1+1+9 → 1x1x1x9=9
(2,1,1,8)= 12 → 2+1+1+8 → 2x1x1x8=16
(2,2,1,7)= 12 → 2+2+1+7 → 2x2x1x7=28
(2,2,2,6)= 12 → 2+2+2+6 → 2x2x2x6=48
(3,2,2,5)= 12 → 3+2+2+5 → 3x2x2x5=60
(3,3,2,4)= 12 → 3+3+2+4 → 3x3x2x4=72
(3,3,3,3)= 12 → 3+3+3+3 → 3x3x3x3=81
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 81 when three numbers are multiplied together.
(3.1,3.1,3.1,2.7)= 12 → 3.1+3.1+3.1+2.7 → 3.1x3.1x3.1x2.7=80.4357
(3.2,3.2,3.2,2.4)= 12 → 3.2+3.2+3.2+2.4 → 3.2x3.2x3.2x2.4=78.6432
I will now move onto fractional numbers as there no decimal number that can give a result higher than 81 using three numbers. I will see in fractional numbers if I can get a number higher than 81 from three fractional numbers.
(3 1/4,3 1/4,3 1/4,2 1/4)= 12 → 3 1/4+3 1/4+3 1/4+2 1/4 → 3 1/4x3 1/4x3 1/4x2 1/4=
77.23828125
(3 2/5,3 1/5,3 1/5,2 1/5)= 12 → 3 2/5+3 1/5+3 1/5+2 1/5 → 3 2/5x3 1/5x3 1/5x2 1/5=
76.5952
I have found that 3,3 and 3 are the three numbers which added together make 12 and when multiplied together make 81 which is the highest possible answer which can be retrieved when three numbers added together equal 12 are multiplied.
13
(1,1,1,10)= 13 → 1+1+1+10 → 1x1x1x10=10
(2,1,1,9)= 13 → 2+1+1+9 → 2x1x1x9 =18
(2,2,1,8)= 13 → 2+2+1+8 → 2x2x1x8 =32
(2,2,2,7)= 13 → 2+2+2+7 → 2x2x2x7 =56
(3,2,2,6)= 13 → 3+2+2+6 → 3x2x2x6 =72
(3,3,2,5)= 13 → 3+3+2+5 → 3x3x2x5 =90
(3,3,3,4)= 13 → 3+3+3+4 → 3x3x3x4 =108
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 108 when three numbers are multiplied together.
(3.1,3.1,3.1,3.7)= 13 → 3.1+3.1+3.1+3.7 → 3.1x3.1x3.1x3.7 =110.2267
(3.2,3.2,3.2,3.4)= 13 → 3.2+3.2+3.2+3.4 → 3.2x3.2x3.2x3.4 =111.4112
(3.3,3.2,3.2,3.3)= 13 → 3.3+3.2+3.2+3.3 → 3.3x3.2x3.2x3.3 =111.5136
(3.25,3.25,3.25,3.25)=13 → 3.25+3.25+3.25+3.25 → 3.25x3.25x3.25x3.25=111.5664063
I will now move onto fractional numbers as there can be no other decimal number that can give a result higher than 111.5664063 using three numbers. I will see in fractional numbers if I can get a number higher than 111.5664063 from three fractional numbers.
(3 1/15,3 5/15,3 4/15,3 5/15)= 13 → 3 1/15+3 5/15+3 4/15+3 5/15 → 3 1/15x3 5/15x
3 4/15,3 5/15=111.308642
(3 1/4,3 1/4,3 1/4,3 1/4)= 13 → 3 1/4+3 1/4+3 1/4+3 1/4 → 3 1/4x3 1/4x3 1/4x
3 1/4=111.5664063
I have found that 3 1/4,3 1/4,3 1/4 and 3 1/4 are the three numbers which added together make 13 and when multiplied together make 111.5664063 which is the highest possible answer which can be retrieved when three numbers added together equal 13 are multiplied.
14
(1,1,1,11)= 14 → 1+1+1+11 → 1x1x1x11=11
(2,1,1,10)= 14 → 2+1+1+10 → 2x1x1x10=20
(2,2,1,9)= 14 → 2+2+1+9 → 2x2x1x9 =36
(2,2,2,8)= 14 → 2+2+2+8 → 2x2x2x8 =64
(3,2,2,7)= 14 → 3+2+2+7 → 3x2x2x7 =84
(3,3,2,6)= 14 → 3+3+2+6 → 3x3x2x6 =108
(3,3,3,5)= 14 → 3+3+3+5 → 3x3x3x5 =135
(3,3,4,4)= 14 → 3+3+4+4 → 3x3x4x4 =144
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 144 when three numbers are multiplied together.
(3.1,3.1,3.9,3.9)= 14 → 3.1+3.1+3.9+3.9 → 3.1x3.1x3.9x3.9=146.1682
(3.3,3.3,3.7,3.7)= 14 → 3.3+3.3+3.7+3.7 → 3.3x3.3x3.7x3.7=149.0841
(3.5,3.5,3.5,3.5)= 14 → 3.5+3.5+3.5+3.5 → 3.5x3.5x3.5x3.5=150.0625
I will now move onto fractional numbers as there can be no other decimal number that can give a result higher than 150.0625 using three numbers. I will see in fractional numbers if I can get a number higher than 150.0625 from three fractional numbers.
(3 4/10,3 4/10,3 6/10,3 6/10)= 14 → 3 4/10+3 4/10+3 6/10+3 6/10 → 3 4/10x3 4/10x
3 6/10x3 6/10=149.8176
(3 1/2,3 1/2,3 1/2,3 1/2)= 14 → 3 1/2+3 1/2+3 1/2+3 1/2 → 3 1/2x3 1/2x3 1/2x3 ½
=150.0625
I have found that 3.5,3.5,3.5 and 3.5 or 3 1/2,3 1/2,3 1/2 and 3 1/2 are the three numbers which added together make 14 and when multiplied together make 150.0625 which is the highest possible answer which can be retrieved when three numbers added together equal 14 are multiplied.
15
(1,1,1,12)= 15 → 1+1+1+12 → 1x1x1x12=12
(2,1,1,11)= 15 → 2+1+1+11 → 2x1x1x11=22
(2,2,1,10)= 15 → 2+2+1+10 → 2x2x1x10=40
(2,2,2,9)= 15 → 2+2+2+9 → 2x2x2x9 =72
(3,2,2,8)= 15 → 3+2+2+8 → 3x2x2x8 =96
(3,3,2,7)= 15 → 3+3+2+7 → 3x3x2x7 =126
(3,3,3,6)= 15 → 3+3+3+6 → 3x3x3x6 =162
(4,3,3,5)= 15 → 4+3+3+5 → 4x3x3x5 =180
(4,4,3,4)= 15 → 4+4+3+4 → 4x4x3x4 =192
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 192 when three numbers are multiplied together.
(3.5,3.5,3.5,4.5)= 15 → 3.5+3.5+3.5+4.5 → 3.5x3.5x3.5x4.5=192.9375
(3.75,3.75,3.75,3.75)= 15 → 3.75+3.75+3.75+3.75 → 3.75x3.75x3.75x3.75
=197.7539062
I will now move onto fractional numbers as there can be no other decimal number that can give a result higher than 197.7539062 using three numbers. I will see in fractional numbers if I can get a number higher than 197.7539062 from three fractional numbers.
(3 1/4,3 1/4,3 1/4,5 1/4)= 15 → 3 1/4+3 1/4+3 1/4+5 1/4 → 3 1/4x3 1/4x3 1/4x5 1/4=
180.2226563
(3 3/4,3 3/4,3 3/4,3 3/4)= 15 → 3 3/4+3 3/4+3 3/4+3 3/4 → 3 3/4x3 3/4x3 3/4x3 3/4=
197.7539062
I have found that 3.75,3.75,3.75 and 3.75 or 3 3/4,3 3/4,3 3/4 and 3 3/4 are the three numbers which added together make 15 and when multiplied together make 197.7539062 which is the highest possible answer which can be retrieved when three numbers added together equal 15 are multiplied.
16
(1,1,1,13)= 16 → 1+1+1+13 → 1x1x1x13=13
(2,1,1,12)= 16 → 2+1+1+12 → 2x1x1x12=24
(2,2,1,11)= 16 → 2+2+1+11 → 2x2x1x11=44
(2,2,2,10)= 16 → 2+2+2+10 → 2x2x2x10=80
(3,2,2,9)= 16 → 3+2+2+9 → 3x2x2x9 =108
(3,3,2,8)= 16 → 3+3+2+8 → 3x3x2x8=144
(3,3,3,7)= 16 → 3+3+3+7 → 3x3x3x7=189
(4,3,3,6)= 16 → 4+3+3+6 → 4x3x3x6=216
(4,4,3,5)= 16 → 4+4+3+5 → 4x4x3x5=240
(4,4,4,4)= 16 → 4+4+4+4 → 4x4x4x4=256
I am now going to use decimal numbers as I have found the highest possible result in whole numbers. I will see in decimal numbers if I can retieve a higher result than 256 when three numbers are multiplied together.
(4.1,4.1,3.9,3.9)= 16 → 4.1+4.1+3.9+3.9 → 4.1x4.1x3.9x3.9=255.6801
(4.2,4.2,3.8,3.8)= 16 → 4.2+4.2+3.8+3.8 → 4.2x4.2x3.8x3.8=254.7216
I will now move onto fractional numbers as there no decimal number that can give a result higher than 256 using three numbers. I will see in fractional numbers if I can get a number higher than 256 from three fractional numbers.
(4 1/5,4 1/5,4 2/5,3 1/5)= 16 → 4 1/5+4 1/5+4 2/5+3 1/5 → 4 1/5x4 1/5x4 2/5x3 1/5=
248.3712
(4 2/9,4 5/9,4 1/9,3 1/9)= 16 → 4 2/9+4 5/9+4 1/9+3 1/9 → 4 2/9x4 5/9x4 1/9x3 1/9=
246.0124981
I have found that 4,4,4 and 4 are the four numbers which added together make 16 and when multiplied together make 256 which is the highest possible answer which can be retrieved when three numbers added together equal 16 are multiplied.
Result of Numbers:
Table of results for quadruplet numbers:
What I Notice:
I notice that the Maxi Product is retrieved when the four parts of the number are multiplied together.
For example, 12, twelve will have a Maxi Product of 81 as a fourth of 12 is 3 and 3 multiplied by itself four times gives you 81. I will now prove this.
Testing my theory:
The maximum product that can be retrieved by 8 is 16. You get this by finding a fourth of 8 and then multiplying itself four times, which is 16. I will prove this now.
(1,1,1,5)= 8 → 1+1+1+5 → 1x1x1x5=5
(2,1,1,4)= 8 → 2+1+1+4 → 2x1x1x4=8
(2,2,1,3)= 8 → 2+2+1+3 → 2x2x1x3=12
(2,2,2,2)= 8 → 2+2+2+2 → 2x2x2x2=16
I will now move on to decimals as I have found the highest result in whole numbers. I will see in decimal numbers if I can retriev a result higher than 16 when four decimal numbers are multiplied.
(2.1,2.1,2.1,1.7)= 8 → 2.1+2.1+2.1+1.7 → 2.1x2.1x2.1x1.7=15.7437
(2.2,2.2,2.2,1.4)= 8 → 2.2+2.2+2.2+1.4 → 2.2x2.2x2.2x1.4=14.9072
I will now move on to use fractions as I have yet not found a number higher than 16. I will see in fractional numbers if I can retriieve a higher number than 16 when four numbers are multiplied together.
(2 5/10,2 2/10,2 1/10,1 2/10)= 8 → 2 5/10+2 2/10+2 1/10+1 2/10 → 2 5/10x2
2/10x2 1/10x1 2/10=13.86
(2 40/100,2 30/100,2 22/100,1 8/100)= 8 → 2 40/100+2 30/100+2 22/100+1 8/100 →
2 40/100+2 30/100+2 22/100=13.234752
I have found that 2,2,2 and 2 are the four numbers, which added together make 8 and when multiplied together make 16 which is the highest possible answer which can be retrieved.
Rule in words:
Maxi Product equals a fourth of the selected number multiplied by itself four times.
Rule in Algebra:
M=(N/4)
Key:
M= Maxi Product
N=Number Selected
Proving my rule:
Find the Maxi Product of a)44 b)55 and c)66.
a) M=(N/4) b) M=(N/4) c) M=(N/4)
M=(44/4) M=(55/4) M=(66/4)
M=14644 M=35744.62891 M=74120.0625
The General Rule:
Rule for doubles → M=(N/2)²
Rule for triples → M=(N/3)³
Rule for Quadruplets→ M=(N/4)
I notice that what ever the number is divided by, it is always then powered by the same number.
For example, if the number were to be split into 6 parts (sextuplets), then the equation for that would be: M=(N/6) .
Rule in words:
Maxi Product equals the number divided by X number of parts and that powered by X.
Rule in Algebra:
M=(N/X)
Key:
M=Maxi Product
N=Number selected
X=Parts it has been split up in e.g. Doubles, triples, etc.
Proving My Rule:
Find the Maxi Product of a) 44 when it’s split up into 7 parts; b) 55 when it’s split up by 8 parts and c) 66 when it’s split up into 9 parts.
a) M=(N/X)
M=(44/7)
M=387688.0863
b) M=(N/X)
M=(55/8)
M=4990931.629
c) M=(N/X)
M=(66/9)
M=61335630.63
