Logic Puzzles

58. Counting Closed Loops

Each four-digit number on the left is transformed into the single digit on the right:

9999 = 4
8888 = 8
1816 = 3
1212 = 0
1919 = ?

What digit should replace the question mark?

Added 16 March 2012

Hint:

Look at the shapes of the digits. How many closed loops (holes) does each digit contain?

Solution:

The rule is to count the number of closed loops in the digits.

  • 9 9 9 9: each 9 has one loop → 4 loops.
  • 8 8 8 8: each 8 has two loops → 8 loops.
  • 1 8 1 6: 8 has two loops, 6 has one → 3 loops.
  • 1 2 1 2: digits 1 and 2 have no loops → 0 loops.

For 1 9 1 9, each 9 contributes one loop and the 1s contribute none, giving 2 loops in total.

Therefore the missing digit is 2.


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