Tile Layout Maths: Centred Borders and Internal Joints

Tile Layout Maths: Centred Borders and Internal Joints

Original quantitative topic practice in English. All 24 questions are included in a shuffled order. Each question supplies its own data and model assumptions; use only those assumptions. Choose one answer. Practice target: 20/24, not an official examination pass mark. Keep full intermediate precision. These exercises cover the calculation scope in the title; they do not constitute a full Red Seal examination, trade qualification, site design or operating specification.
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A rectangular tiling field is 2750×3650 mm after perimeter gaps have already been deducted. Square tiles have side 300 mm; internal joints are 5 mm. For this exercise choose full interior tiles across an axis as floor((field+j)/(tile+j))−1, then use two equal cut borders. There are n+1 joints around n full interior tiles. Each edge or corner piece consumes its own tile; reuse of offcuts is excluded. Calculate the tiles consumed under the no-offcut-reuse rule. Keep intermediate values unrounded; round the final answer to 4 decimal places if needed.