can-you-find-any-arrangement-of-nine-digits-of-1-9-such-as-967854312-and-the-first-digit-should-be-divisible-by-1-thefirst-two-digitds-should-be-divisible-by-2-the-first-three-digitds-should-be-divisi

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Question Number 208555 by liuxinnan last updated on 18/Jun/24

can you find any arrangement of nine digits of 1−9 such as 967854312 and the first digit should be divisible by 1 thefirst two digitds should be divisible by 2 the first three digitds should be divisible by 3 ...... the number should be fivisible by 9 if is such a number available

c a n y o u f i n d a n y a r r a n g e m e n t o f n i n e d i g i t s o f 1 - 9

s u c h a s 967854312

a n d t h e f i r s t d i g i t s h o u l d b e d i v i s i b l e b y 1

t h e f i r s t t w o d i g i t d s s h o u l d b e d i v i s i b l e b y 2

t h e f i r s t t h r e e d i g i t d s s h o u l d b e d i v i s i b l e b y 3

\dots \dots

t h e n u m b e r s h o u l d b e f i v i s i b l e b y 9

i f i s s u c h a n u m b e r a v a i l a b l e

Answered by nikif99 last updated on 18/Jun/24

5th digit is 5. 2nd, 4th, 6th, 8th digits are even. 1st, 3rd, 7th, 9th digits are odd. 4th is 2 or 6 (ending in 12, 16, 32, 36...) (1st+2nd+3rd) as well (4th+5th+6th) must be divided by 3. ... By eliminating some cases and “try and check”, you reach 381654729. PS. Then, you add a 0 and you obtain a number duvisible by 10.

5 t h d i g i t i s 5 .

2 n d, 4 t h, 6 t h, 8 t h d i g i t s a r e e v e n .

1 s t, 3 r d, 7 t h, 9 t h d i g i t s a r e o d d .

4 t h i s 2 o r 6 (e n d i n g i n 12, 16, 32, 36 \dots)

(1 s t + 2 n d + 3 r d) a s w e l l (4 t h + 5 t h + 6 t h)

m u s t b e d i v i d e d b y 3 .

\dots

B y e l i m i n a t i n g s o m e c a s e s a n d “ t r y

a n d {c h e c k}^{″}, y o u r e a c h 381654729 .

P S . T h e n, y o u a d d a 0 a n d y o u o b t a i n

a n u m b e r d u v i s i b l e b y 10 .

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