License Plates Madness

Logic Level 3

A car accident victim, still under shock, was not able to remember the exact license plate of the car which ran him over. All he could remember was that it was composed by two letters, three numbers and again two letters, as displayed above. The letters, X X , can be described as numbers going from A = 1 A=1 to Z = 26 Z=26 . The numbers, N N , are all positive integers that go from 1 to 9, 0 is not included. Knowing that, the man said that:

  • The sum of the first letter and the first number is equal to 7.
  • The second letter divided by the third number is equal to 4.
  • The first number minus the first letter is equal to the second number.
  • The fourth letter was a 4.
  • The third letter minus the third number is equal to 4.
  • The first letter was an "A".
  • The Second Letter was two times the first number.

Enter your answer under number form (eg: if you think the license plate number is ZB-974-JL, you'd have to enter 2629741012).


The answer is 11265374.

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1 solution

Roberto Gallotta
Jan 13, 2016

Let

X X N N N X X
L1 L2 N1 N2 N3 L3 L4

and let's rewrite the properties of the license plate:

  1. L1 + N1 = 7

  2. L2/N3 = 4

  3. N1 - L1 = N2

  4. L4 = 4

  5. L3 - N3 = 4

  6. L1 = 1

  7. L2 = 2xN1

Since L1 = 1, then N1 = 7 - 1 = 6.

N2 = N1 - L1 = 6 - 1 = 5.

L2 = 2 x N1 = 2 x 6 = 12.

N3 = L2/N3 = 12/4 = 3.

L3 = 4 + N3 = 7.

So, the correct answer is 11265374 (or, with the actual letters AL653GD).

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