# The Fact Families 2x3=6 And 2x10=20 Contain Exactly 3 Different Digits. How Many Other Fact Families With Dividends Under 100 Contain Exactly 3 Different Digits?

36 is the total number of fact families with three different digits and a dividend less than 100. However, the question asks "how many other fact families", so you have to subtract out the two given in the question. 36-2=34

Last part of the question relates to the first two examples so the answers would be 3x2=6 and 10x2=20
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This 3rd grade homework question is evil.
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2*3=6
2*4=8
2*5=10
2*6=12
2*7=14
2*8=16
2*9=18
2*10=20
3*4,3*5, 3*6, 3*7,3*8,3*9,3*10,4*5,...4*10
if you notice for 2-table, 8, and for 3-table its 7, and for4-table its 6..
So 8+7+6+5+4+3+2+1, here 10-table can  be easily excluded, hence the answer is 36
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Dividends under 100, so you should consider 2*11=22...... 2*48=96.      So isn't it 131 (Well -2 so 129)?This is hard....
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64
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There are 102 such families. 64 of those are of the form 1*(2-digit number) = (2-digit number). Here's a list.
{9, 10, 90}, {9, 9, 81}, {8, 10, 80}, {8, 8, 64}, {7, 10, 70}, {7, 7, 49},
{6, 16, 96}, {6, 10, 60}, {6, 8, 48}, {5, 19, 95}, {5, 15, 75}, {5, 10, 50},
{5, 9, 45}, {5, 7, 35}, {4, 22, 88}, {4, 16, 64}, {4, 10, 40}, {4, 6, 24},
{4, 4, 16}, {3, 31, 93}, {3, 30, 90}, {3, 22, 66}, {3, 13, 39}, {3, 10, 30},
{3, 5, 15}, {2, 44, 88}, {2, 42, 84}, {2, 33, 66}, {2, 26, 52}, {2, 25, 50},
{2, 24, 48}, {2, 21, 42}, {2, 20, 40}, {2, 12, 24}, {2, 10, 20}, {2, 6, 12},
{2, 4, 8}, {2, 3, 6}, {1, 98, 98}, {1, 97, 97}, {1, 96, 96}, {1, 95, 95},
{1, 94, 94}, {1, 93, 93}, {1, 92, 92}, {1, 90, 90}, {1, 89, 89}, {1, 87, 87},
{1, 86, 86}, {1, 85, 85}, {1, 84, 84}, {1, 83, 83}, {1, 82, 82}, {1, 80, 80},
{1, 79, 79}, {1, 78, 78}, {1, 76, 76}, {1, 75, 75}, {1, 74, 74}, {1, 73, 73},
{1, 72, 72}, {1, 70, 70}, {1, 69, 69}, {1, 68, 68}, {1, 67, 67}, {1, 65, 65},
{1, 64, 64}, {1, 63, 63}, {1, 62, 62}, {1, 60, 60}, {1, 59, 59}, {1, 58, 58},
{1, 57, 57}, {1, 56, 56}, {1, 54, 54}, {1, 53, 53}, {1, 52, 52}, {1, 50, 50},
{1, 49, 49}, {1, 48, 48}, {1, 47, 47}, {1, 46, 46}, {1, 45, 45}, {1, 43, 43},
{1, 42, 42}, {1, 40, 40}, {1, 39, 39}, {1, 38, 38}, {1, 37, 37}, {1, 36, 36},
{1, 35, 35}, {1, 34, 34}, {1, 32, 32}, {1, 30, 30}, {1, 29, 29}, {1, 28, 28},
{1, 27, 27}, {1, 26, 26}, {1, 25, 25}, {1, 24, 24}, {1, 23, 23}, {1, 20, 20}
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