58. Counting Closed Loops Each four-digit number on the left is transformed into the single digit on the right:9999 = 48888 = 81816 = 31212 = 01919 = ?What digit should replace the question mark? Added 16 March 2012 Show Hint Show Solution 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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