A Puzzle A Day: 2026-04-15

Correct: 6327

Let's break down the four-digit labels (ABCD) into two two-digit numbers (AB and CD) and analyze their patterns: **Part 1: The first two digits (AB)** Observe the sequence for AB: 18, 36, 45, 54. These numbers are multiples of 9: * 18 = 9 × 2 * 36 = 9 × 4 * 45 = 9 × 5 * 54 = 9 × 6 The multipliers are 2, 4, 5, 6. The differences between these multipliers are (+2, +1, +1). Following this progression, the next difference should be +1. So, the next multiplier for Painting 5 would be 6 + 1 = 7. Therefore, the first two digits for Painting 5 (AB) = 9 × 7 = 63. (A quick check: The sum of digits A+B for all paintings is always 9 (1+8=9, 3+6=9, 4+5=9, 5+4=9). For 63, 6+3=9, so this part of the pattern is consistent). **Part 2: The last two digits (CD)** Observe the sequence for CD: 27, 12, 09, 06. This sequence splits based on whether the painting number is odd or even: * **For odd-numbered paintings (P1, P3):** The CD values are 27 and 09. This is an alternating pattern. For P1 it's 27, for P3 it's 09. Thus, for P5 (the next odd-numbered painting), the CD value will be 27. (Check: The sum of digits C+D for odd paintings is always 9 (2+7=9 for P1, 0+9=9 for P3). For 27 (P5), 2+7=9, which is consistent). * **For even-numbered paintings (P2, P4):** The CD values are 12 and 06. This is a sequence where each number is 6 less than the previous (12 - 6 = 06). The next even-numbered painting (P6) would have CD = 06 - 6 = 00. (Check: The sum of digits C+D for even paintings is 3 for P2 (1+2=3) and 6 for P4 (0+6=6). This follows a pattern of 3 times the painting number divided by 2 (3*(2/2)=3, 3*(4/2)=6). For P6, 3*(6/2)=9, while 0+0=0, showing that the number sequence 12, 06, 00 is primary over the sum-of-digits for even paintings in this specific tricky puzzle). Combining both parts, the label for Painting 5 is 6327. **Why other choices are incorrect:** * **6303:** While the first two digits (63) are correct, the last two digits (03) sum to 3. For an odd painting (P5), the sum of the last two digits should be 9 based on the established pattern (27, 09 sums to 9). This choice might arise from seeing a pattern of adding 897 (5406 + 897 = 6303), but this contradicts the consistent sum-of-digits rule for odd paintings. * **7209:** The first two digits (72) are incorrect as they do not follow the derived pattern of 9 times the sequential multiplier (9x7=63, not 72). Also the CD value would be 09, while the alternating pattern would point to 27 for P5. * **6318:** While the first two digits (63) are correct, and the last two digits (18) sum to 9 (2+7=9), this specific CD value (18) does not follow the alternating sequence of 27, 09 for odd paintings.