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Consider two positive even integers less than 15 (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?

 Jan 17, 2018
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[2 +2] +  2*2  =  8             [4 + 4] + 4*4  = 24          [ 6 + 6 ] + 6*6  = 48

[2 + 4]  + 2*4  = 14           [4 + 6] +  4*6  = 34          [6 + 8 ]  +  6*8  =  62

[2 + 6] +  2*6  =  20          [4 + 8 ] + 4*8  = 44          [ 6 + 10] + 6*10  = 76

[2 + 8]  +  2*8  = 26          [4 + 10 ] + 4*10  = 54      [6 + 12] + 6*12  = 90

[2 + 10] + 2*10  =  32       [ 4 + 12] + 4*12  = 64      [6 + 14] + 6 * 14 = 104

[2 + 12] + 2*12  = 38        [4 + 14 ] + 4*14  = 74

[ 2 + 14] + 2*14  = 44

 

[8 + 8 ]  + 8* 8  =  80         [ 10 + 10] + 10*10  = 120     [12 + 12] + 12*12 = 168

[ 8 + 10] + 8*10  = 98        [10 + 12] + 10*12  =  142     [ 12 + 14] +  12*14  = 194

[8 + 12] + 8*12  = 116       [10 + 14] + 10*14 =   164

[8 + 14]  + 8*14 = 134

 

[14 + 14]  +  14*14  =  224

 

 

Total  different values  =  7 + 5 + 5 + 4 + 3 + 2 + 1  =     27

 

 

cool cool cool

 Jan 17, 2018
edited by CPhill  Jan 17, 2018

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