Spy vs Spy

[bbrown88]

To enter a secure door, two numbers are displayed and the person trying to gain access must enter a third number. The first two numbers relate to the 3rd number. A spy watching saw when 1 and 2 were displayed, 9 was entered. When 3 and 4 were displayed, 20 was entered. And when 5 and 6 were displayed, 12 was entered. The spy goes up to the door and finds 17 and 12 displayed. What number must he enter to gain access?

[gabeshep]

54

[bernardo]

why 54?

[gabeshep]

this is how i came up with 54: in each case, the number of LETTERS in the first two numbers is multiplied to give the third number. i.e., 1 and 2, when spelled out ('ONE and TWO') contain 3 letters each. 3 times 3 is 9. in the same way, 'THREE' has 5 letters and 'FOUR' has 4 letters - 5 times 4 is 20. again, 'FIVE' (4 letters), 'SIX' (3 letters) - 4 times 3 is 12. finally, 'SEVENTEEN' has 9 letters and 'TWELVE' has 6, so 9 times 6 makes 54.