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Question Number 114295 by mathdave last updated on 18/Sep/20

	Answered by mr W last updated on 19/Sep/20

	$s a y t h e n u m b e r i s [a b c d e]$ $l e t A = a + c + e$ $B = b + d$ $A + B = 41 (a s g i v e n)$ $A - B = 0 o r \pm 11, \pm 22, . . .$ $\Rightarrow A = 20, B = 21 (i m p o s s i b l e, s i n c e B < 2 \times 9 = 18)$ $\Rightarrow A = 26, B = 15$ $\Rightarrow A = 37, B = 4 (i m p o s s i b l e, s i n c e A < 3 \times 9 = 27)$ $s o w e h a v e o n l y o n e p o s s i b i l i t y :$ $A = 26, B = 15$ $\Rightarrow A = 9 + 9 + 8$ $\Rightarrow B = 9 + 6$ $\Rightarrow s m a l l e s t n u m b e r i s 86999$ $\Rightarrow l a r g e s t n u m b e r i s 99968$
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