Find the sum of all three digit numbers started with odd number when each digit are different. Please help...


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Question Number 188879 by Nimnim111118 last updated on 08/Mar/23

$F i n d t h e s u m o f a l l t h r e e d i g i t n u m b e r s$ $s t a r t e d w i t h o d d n u m b e r w h e n e a c h d i g i t$ $a r e d i f f e r e n t .$ $P l e a s e h e l p . . .$
Commented by mr W last updated on 08/Mar/23

$d o y o u k n o w t h e a n s w e r ?$
Commented by Nimnim111118 last updated on 08/Mar/23

$S o r r y, I d o n t k n o w t h e a n s w e r .$ $i n f a c t, I h a v e n o i d e a$
Commented by mr W last updated on 09/Mar/23

$i h o p e m y s o l u t i o n b e l o w c o u l d h a v e$ $h e l p e d y o u .$
	Answered by mr W last updated on 09/Mar/23

	$a x y$ $x a y$ $x y a$ $[100 \times 9 \times 8 + 10 \times 8 \times 8 + 8 \times 8] (1 + 2 + 3 + . . . + 9)$ $= 355 680 ✓$
	Commented by Nimnim111118 last updated on 08/Mar/23

	$T h a n k y o u s o m u c h .$ $B u t s t i l l I d o n t g e t t h e i d e a . . .$
	Commented by Nimnim111118 last updated on 08/Mar/23

	$I n m y o p i n i o n :$ $R e q u i r e d : ∙ s u m o f a l l 3 d i g i t$ $∙ a l l n u m b e r s t a r t e d b y o d d$ $∙ n o d i g i t a r e r e p e a t e d$ $S o, o u r q u e s t i o n i s l i k e k y t o b e a d d e d u p$ $t h e f o l o w i n g$ $102 + 103 + 104 + 105 + 106 + 107 + 108 + 109$ $+ 120 + 123 + 124 + 125 + 126 + 127 + 128 + 129$ $+ 130 + 132 + 134 + 135 + 136 + 137 + 138 + 139$ $a n d i t w i l l g o u p t o$ $980 + 981 + 982 + 983 + 984 + 985 + 986 + 987$
	Commented by mr W last updated on 09/Mar/23

	$i n t h i s w a y y o u s u m u p a l l t h e v a l i d$ $n u m b e r s .$ $b u t i^{'} m t o o l a z y t o d o t h i s h a r d w o r k .$ $i n s t e a d o f t h i s i s u m u p a l l t h e d i g i t s$ $i n t h e n u m b e r s . t h i s i s e a s i e r, b e c a u s e$ $w e h a v e m a n y m a n y n u m b e r s, b u t$ $o n l y 9 d i g i t s .$
	Commented by mr W last updated on 08/Mar/23

	$i n m y s o l u t i o n a b o v e i c o n s i d e r e d$ $a l l 3 d i g i t n u m b e r s w i t h d i f f e r e n t$ $d i g i t s, a l s o n u m b e r s s t a r t i n g w i t h a n$ $e v e n d i g i t, l i k e 235 . i f y o u m e a n o n l y$ $n u m b e r s s t a r t i n g w i t h a n o d d d i g i t,$ $t h e n i m u s t m o d i f y m y s o l u t i o n .$
	Answered by mr W last updated on 09/Mar/23

	$w h e n w e w a n t t o g e t t h e s u m o f s o m e$ $n u m b e r s, e . g . 123 + 456, w e c a n a l s o g e t$ $t h e r e s u l t b y s u m m i n g u p t h e v a l u e s$ $w h i c h t h e i n d i v i d u a l d i g i t s r e p r e s e n t .$ $i n t h i s e x a m p l e, t o g e t 123 + 456, w e$ $c a n p r o c e e d l i k e t h i s :$ $100 \times (1 + 4) + 10 \times (2 + 5) + 1 \times (3 + 6)$ $= 500 + 70 + 9$ $= 579$ $t o s u m u p a l l 3 d i g i t n u m b e r s w h i c h$ $s t a r t w i t h a n o d d d i g i t a n d c o n s i s t$ $o f 3 d i f f e r e n t d i g i t s, w e c a n u s e t h i s$ $m e t h o d .$ $t o g e t t h e s u m o f a l l v a l u e s w h i c h$ $t h e d i g i t ‘ ‘ a ‘ ‘ r e p r e s e n t s i n a l l$ $s u c h 3 d i g i t n u m b e r s :$ $\underset{―}{t y p e a x y :}$ $a = 1, 3, 5, 7, 9$ $f o r e a c h ‘ ‘ a^{″} t h e r e a r e 9 \times 8 n u m b e r s,$ $100 \times 9 \times 8 \times (1 + 3 + 5 + 7 + 9) = 180 000$ $\underset{―}{t y p e x a y :}$ $a = 1, 3, 5, 7, 9 o r 2, 4, 6, 8$ $x = 1, 3, 5, 7, 9$ $10 \times 4 \times 8 \times (1 + 3 + 5 + 7 + 9)$ $+ 10 \times 5 \times 8 \times (2 + 4 + 6 + 8) = 16 000$ $\underset{―}{t y p e x y a :}$ $s i m i l a r l y t o t y p e x a y .$ $1 \times 4 \times 8 \times (1 + 3 + 5 + 7 + 9)$ $+ 1 \times 5 \times 8 \times (2 + 4 + 6 + 8) = 1 600$ $a l l t o g e t h e r :$ $180 000 + 16 000 + 1 600 = 197 600 ✓$ $t h a t m e a n s t h e r e a r e t o t a l l y$ $5 \times 9 \times 8 = 360 s u c h n u m b e r s, a n d t h e$ $s u m o f t h e m i s 197 600 .$
	Commented by mr W last updated on 08/Mar/23

	$m a y b e B r a n d o n s i r c a n c h e c k t h i s$ $r e s u l t w i t h a p r o g r a m .$
	Commented by ARUNG_Brandon_MBU last updated on 09/Mar/23

	Commented by ARUNG_Brandon_MBU last updated on 09/Mar/23
	#include <iostream> using namespace std; int main(void) { short count=0; int sum=0; for (short i0, i1, i2, i=102; i<1000; i++) { i0 = i / 100; i1 = i % 100 / 10; i2 = i % 10; if (i0%2==1&&i0!=i1&&i0!=i2&&i1!=i2) { sum += i; count++; } } cout << "There are " << count << "numbers"; cout << "\n their sum is " << sum; return 0; }
	Commented by ARUNG_Brandon_MBU last updated on 09/Mar/23

	Commented by mr W last updated on 09/Mar/23

	$g r e a t p r o g r a m i n g! t h a n k s a l o t s i r!$
	Commented by ARUNG_Brandon_MBU last updated on 09/Mar/23
	You're welcome, Sir ��
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