How many positive four-digits integers abcd satisfy the following conditions: (i) abcd is divisible hy 7; (ii) When the first and the last digits are interchanged, the resulting number dbca is still a positive four-digits number that is divisible by 7.


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Question Number 124824 by ZiYangLee last updated on 06/Dec/20

$How many positive four - digits integers$ $a b c d satisfy the following conditions :$ $(i) a b c d is divisible hy 7;$ $(ii) When the first and the last digits$ $are interchanged, the resulting number$ $d b c a is still a positive four - digits number$ $that is divisible by 7 .$
Commented by mr W last updated on 06/Dec/20

$a b c d m u s t b e d i f f e r e n t d i g i t s ?$
Commented by ZiYangLee last updated on 06/Dec/20

$w e l l a s t h e o r i g i n a l q u e s t i o n d o e s n o t$ $m e n t i o n i t, i t h i n k a b c d c a n b e s a m e$ $d i g i t s a l s o (?$
Commented by mr W last updated on 06/Dec/20

$t h e n$ $(i)$ $1001, 1008, 1015, . . ., 9996$ $\Rightarrow 1 + \frac{9996 - 1001}{7} = 1286 n u m b e r s$
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