Refer to the following series and answer the question. (Counting to be done from left to right only.) (All numbers are single-digit numbers only.) (Left) 9 7 6 4 3 5 7 6 4 6 7 6 9 8 7 7 6 6 7 6 5 7 6 8 7 5 6 (Right) How many such even digits are there, each of which is immediately preceded by a perfect square and immediately followed by an even digit? (NOTE: 1 is also a perfect square)
None
Single-digit perfect squares: 1, 4, 9. Even single digits: 2, 4, 6, 8.
Number the positions 1 to 27: 9(1) 7(2) 6(3) 4(4) 3(5) 5(6) 7(7) 6(8) 4(9) 6(10) 7(11) 6(12) 9(13) 8(14) 7(15) 7(16) 6(17) 6(18) 7(19) 6(20) 5(21) 7(22) 6(23) 8(24) 7(25) 5(26) 6(27).
Scan for even digits and check both conditions:
Pos 3 = 6 (even): preceded by 7 (not a perfect square) ✗
Pos 4 = 4 (even): preceded by 6 (not a perfect square) ✗
Pos 8 = 6 (even): preceded by 7 (not a perfect square) ✗
Pos 9 = 4 (even): preceded by 6 (not a perfect square) ✗
Pos 10 = 6 (even): preceded by 4 ✓ (perfect square); followed by 7 (odd) ✗
Pos 12 = 6 (even): preceded by 7 (not a perfect square) ✗
Pos 14 = 8 (even): preceded by 9 ✓ (perfect square); followed by 7 (odd) ✗
Pos 17 = 6 (even): preceded by 7 (not a perfect square) ✗
Pos 18 = 6 (even): preceded by 6 (not a perfect square) ✗
Pos 20 = 6 (even): preceded by 7 (not a perfect square) ✗
Pos 23 = 6 (even): preceded by 7 (not a perfect square) ✗
Pos 24 = 8 (even): preceded by 6 (not a perfect square) ✗
Pos 27 = 6 (even): preceded by 5 (not a perfect square) ✗
No position satisfies all three conditions simultaneously: the even digit is preceded by a perfect square AND followed by an even digit.
Hence, the count is None.
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