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Bridgehead Systems A bridgehead system is a group of simple lines of the form ) , where numbers a are h distinct fixed i h numbers (showing in each line), and the last p – h numbers ( x j ) are obtained through the unfolding of all p – h -size combinations of the remaining playing numbers (m – h numbers). Obviously, 1 ≤ h ≤ p . Parameter h will refer to the number of fixed numbers of the system; p – h will refer to the number of variable numbers of the system (being in fact the size of the combinations of numbers xj ). (a a a x x x 1 2 h h+1 h+2 p p−h For counting the number of simple lines of such a system, we shall count the combinations of numbers x , which number C p−h . j m−h Let us make the following immediate observations: 1) Numbers ai and xj cover all the m playing numbers. 2) The set of numbers ( ai ) and ( x j ) are exclusive (any number ai is not found among numbers xj and conversely). Here is an example (already presented in a previous chapter) of a bridgehead system in the 6/49 matrix: 123456 123457 123458 ..................... 1 2 3 4 5 49 123467 123468 123469 ..................... 1 2 3 4 6 49 ..................... 1 2 3 4 4849 49PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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