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Find the number of six-digit numbers, where the sum of the digits is divisible by 8.

 Mar 22, 2023
 #1
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100 000    to   999 999   is   900 000 numbers altogether

 

6 numbers that add to 8

 

The sum will be teween  8 and   54

so the sum could be   8,16,24,32,40,48,

 

800 000

710 000

620 000

611 000

530 000

521 000

511 100

440 000

432 000

431 100

422 000

421 100

411 110

332 000

331 100

322 100

321 110

311 111

222 200

222 110

221 111

 

There is an awflu lot to count. I guess there is a better method

970 000

961 000

952 000

951 100

943 000

942 100

941 110

933 100

932 110

931 111

922 210

922 111

...

 

-----------------------

 

The sum of  the 6 digits must be between 1 and 54  

6 of those are divisable by 8

If they were all equally likely outcomes then the answer would be  6/54. Trouble is they are not all equally likely outcomes.

 

there are 900 000 sums altogether.   Ifthey were equally likely it would be   6/54 * 900 000 = 100 000  but they are not equally likely.

 

Yea, I don't know.   wink

 Mar 22, 2023
edited by Melody  Mar 22, 2023
 #2
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10 - 99 : 11
100 - 999 : 112
1000 - 9999 : 1124
10000 - 99999 : 11248
100,000 - 999,999 : 112,496
1000000 - 9999999 : 1124992
10000000 - 99999999 : 11249985
100000000 - 999999999 : 112499976
1000000000 - 9999999999 : 1124999972

 Mar 22, 2023

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