16. The digits 0 to 9 can be drawn with horizontal and vertical segments, as shown. Greg chooses three different digits. In total, his digits have 5 horizontal segments and 10 vertical segments. What is the sum of his three digits?

A 9
B 10
C 14
D 18
E 19
Solution
A

The number of horizontal segments in Greg's three digits is five. Since the maximum number of horizontal segments in any digit is three, these five segments could be arranged as 0,2 and 3 or 1,1 and 3 or 1,2 and 2 . However, only the digit 0 has two horizontal segments so an arrangement using three different digits with 1,2 and 2 horizontal segments is not possible. There are two different digits with one horizontal segment, namely 4 and 7 , but these only contain a total of five vertical segments leaving the third digit needing five vertical segments when only a maximum of four is possible. Therefore the only possible arrangement of horizontal segments is 0,2 and 3 . Only the digit 1 has no horizontal segments and, as mentioned earlier, only the digit 0 has two horizontal segments. Between them the digits 1 and 0 have six vertical segments and hence the third digit has three horizontal segments and four vertical segments and only digit 8 satisfies these conditions. Therefore the sum of Greg's three digits is $0+1+8=9$.