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 Missing digits (Posted on 2011-06-06)
Replace the interrogation marks in the following statements by appropriate digits (0 to 9) to make these statements valid:

D1: 34?561? is exactly divisible by 45
D2: 68??37 is exactly divisible by 99
D3: 9???057 is equal to 417 times ?1???
D3: 70??34? is exactly divisible by 792
D4: 4?18? is exactly divisible by 101
D5: 6?80?8??51 is exactly divisible by 73*137

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 D5 by hand | Comment 5 of 8 |

6a80b8cd51 is divisible by 73*137=10001

6a80b8cd51 = 10001*efghij, so e=6, j=1

6a80b8cd51 = 10001*6fghi1 = 10001*600001 + 10001*fghi0 = 6000610001 + 10001*fghi0

a80b8cd5 = 61000 + 10001*fghi, so i=5

a80b8cd = 11100 + 10001*fgh, so h=d

a80b8c = 1110 + 10001*fg + 1000d, so g=c

a80b8 = 111 + 10001f + 1000c + 100d, so f=7

a80b = 7011 +100c +10d, so b=1

a80 = 701 + 10c +d, so d=9

a8 = 71 + c, so c=7, a=7

6780187951 is divisible by 73*137

 Posted by xdog on 2011-06-06 21:59:04

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