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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 simpler | Comment 6 of 8 |
73*137=10001 so set up a long multiplication as for D4.
`    abcdefx    10001     abcdefabcdef    6?80?8??51Clearly a=6, e=5, f=1 and three of the question marks are b, c, d.    6bcd51x    10001     6bcd516bcd51    6b80?8cd51`

b+1=8 so b=7, 6+5 gives the last ? which is a 1, 1+d ends in 0 so d=9, 1+c=8 so c=7.

`    677951x    10001     677951677951    6780187951`

 Posted by Jer on 2011-06-07 10:16:13

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