Answer: 9 (so the number is 12349678)


Using division

 
The number is divisible by 11 so there must have been a remainder of 8 to give 88
 

___7 gives a remainder of 8
107 = 99 + 8


___6 gives a remainder of 10

76 = 66 + 10


 2__ gives a remainder of 7
22 + 7 = 29
9 is missing


Using a divisibility test
A test for divisibility by 11 is to add alternate digits:

1 + 3 + * + 7 = 11 + *; 2 + 4 + 6 + 8 = 20.

If the original number is a multiple of 11 then these two totals will be the same or will differ by a multiple of 11. In this case, 11 + * = 20 gives * = 9.

Using place value and algebra

1234*678 = 12340678 + 1000* = (11 x 1121879 +9) + 11 x 90* + 10*

and hence is divisible by 11 if and only if 10* + 9 is divisible by 11. So * = 9.