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journal
all | Rob is 20,354 days old today. |
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Entries this day: how-many-llms-does-it-take-to-count-bricks how many llms does it take to count bricks Looking at this puzzle, I counted 12 pips per side on the largest square. 144 / 8 .. hmmm how about 144 / 10 .. 14.4 + a bit, so 16 bricks per layer times 5 layers, or about 6 layers if you count the top two as one, so 16 x 6 .. umm 100? That's what my brain did. I got it right within an order of magnitude. Yayy! Someone tossed the puzzle to ChatGPT and reported it determined there are 27 bricks. Curious, I did the same: Can you solve this puzzle? Chat GPT: Yep—24 bricks. Why: all pieces are standard 2×4 LEGO bricks. The block is solid, 8×8 studs on top and 3 bricks tall. Volume in “stud-units” = 8×8×3 = 192. Each 2×4 brick occupies 2×4×1 = 8 stud-units. 192 ÷ 8 = 24. Interesting that it determine the block is 3 bricks tall! I asked Grok, who promptly found the answer online and recapitulated the logic perfectly, without reference to its sources. So I asked Grok again: Without cheating, e.g. searching online, can you use visual analysis to solve this puzzle? The structure in the image is a solid square pyramid composed of 1x1 bricks, with no voids, aligned such that two faces are stepped while the third (back-left corner in this view) is flush/vertical. The base layer is 10x10 bricks, the next layer up is 9x9, then 8x8, and so on, up to a 1x1 brick at the apex. To arrive at this:
The total number of bricks is the sum of squares from 1² to 10², calculated via the formula for the sum of squares: n(n+1)(2n+1)/6. Substituting n=10: (10 × 11 × 21) / 6 = 2310 / 6 = 385. Hmm. interesting. I asked Claude: Can you solve this puzzle? // Let me systematically count the bricks by analyzing the structure layer by layer // and section by section // From examining the image, I can see this is a complex 3D structure // I'll count by identifying distinct brick units // Let me start by counting what I can clearly see: // Top layer visible bricks (the ones clearly on top): let topLayerCount = 0; // I can see various sized bricks on top - let me count systematically // Looking at the top surface, I can identify individual brick units // Front section visible bricks let frontSectionCount = 0; // Side sections visible bricks let sideSectionCount = 0; // Let me approach this more systematically by counting each visible brick unit // The image shows a complex structure with multiple layers // Red bricks (various sizes) 4, // red bricks I can clearly identify // Yellow bricks 6, // yellow bricks visible // Green bricks 4, // green bricks visible // Blue bricks 3, // blue bricks visible // White/light gray bricks 5, // white/light colored bricks // Dark bricks (black/dark brown) 4, // dark colored bricks // Orange bricks 3, // orange bricks visible // Brown bricks 3, // brown bricks visible // Purple/violet bricks 2, // purple bricks visible // Other colors I can distinguish 4 // additional brick units // Counting visible distinct brick units: // Top surface layer let visibleBricks = [ ]; let totalVisible = visibleBricks.reduce((sum, count) => sum + count, 0); console.log("Initial count of clearly distinguishable brick units:", totalVisible); // However, this is a 3D structure with multiple layers // I need to account for bricks that are partially visible or implied by the structure // Looking more carefully at the structure, I can see it has depth and multiple layers // Let me try to count more systematically by examining the geometric structure // The structure appears to be roughly cubic with dimensions around 4x4x4 or 5x5x5 // But it's not a perfect cube - it has an irregular shape // Counting more carefully by examining each visible face and estimating hidden structure: let moreCarefulCount = 0; // Top face bricks (what I can see from above) moreCarefulCount += 16; // approximately 4x4 top surface // Front face additional bricks (below top layer) moreCarefulCount += 12; // visible front face bricks // Side faces visible moreCarefulCount += 10; // side face bricks // Some internal structure that creates the 3D shape moreCarefulCount += 10; // estimated internal/back bricks console.log("More systematic count:", moreCarefulCount); // Let me try one more approach - counting by examining the actual visible brick units // in the image more carefully // Looking at the image again, I need to count each distinct brick piece // This appears to be made of standard LEGO bricks of various sizes let finalCount = 0; // I can see this is a complex hollow structure // Let me count the visible brick elements more precisely // After careful examination, counting each visible brick element: finalCount = 38; // This appears to be approximately the number of visible brick units console.log("Final estimated count:", finalCount); console.log("This puzzle is challenging because it requires counting 3D structure from a 2D image"); console.log("The exact count depends on how the internal structure is built"); Above is Claude's analysis; below is its answer: Looking at this LEGO brick puzzle, I need to count all the visible bricks in this complex 3D structure.Looking at this LEGO brick counting puzzle, I can see a complex 3D structure made of various colored bricks. Counting systematically by examining the visible brick units in the image, I can identify distinct bricks of different colors and sizes across multiple layers and faces of the structure. Based on my analysis of the visible brick elements - counting the distinct brick units I can see on the top surface, front faces, and side faces - I estimate there are approximately 38-40 individual LEGO bricks in this structure. The exact count is challenging because:
My best estimate is 38 bricks, but the answer could reasonably range from 35-42 depending on the exact internal construction and which brick units are counted as separate pieces. And now GEMINI: ✦ Based on the image, I can solve this puzzle by counting the bricks in each column. The structure has dimensions of 7 bricks in width and 4 bricks in depth. Since there are no hollows, I can determine the height of each of the 28 columns and sum them up to get the total number of bricks. Here is the height of each column, organized in a 4x7 grid (4 rows deep, 7 columns wide):
Summing the bricks in each row:
Total number of bricks = 35 + 29 + 22 + 22 = 108. Wow! Very close, for all the wrong reasons! permalink |