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Teaching Case — A Rack That Fits and Cannot Be Powered

Eight compute nodes in a 42U cabinet, every one in a unit of its own, nothing overhanging — an elevation that is correct in every way a drawing can be. It draws 5,280 W against a 4,000 W budget, and there is no arrangement of boxes that shows it: twenty servers fit in a rack whether they draw 4 kW or 14 kW, and the elevation is identical either way. Stated per device and per rack, it is exact arithmetic with no heuristics in it.

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Rack D4 — dense compute42U · 25 free · 5,280 of 4,000 W · 217 of 800 kg424140393837363534333231302928272625242322212019181716151413121110987654321ToR switch320 W · 9 kgCompute node 01620 W · 26 kgCompute node 02620 W · 26 kgCompute node 03620 W · 26 kgCompute node 04620 W · 26 kgCompute node 05620 W · 26 kgCompute node 06620 W · 26 kgCompute node 07620 W · 26 kgCompute node 08620 W · 26 kgEvery device is in a unit of its own, and the rack is over its power budget — which no arrangement of boxescould show.ERRORThe declared draw is 5,280 W against a power budget of 4,000 W: 1,280 W over. Twenty servers fit in a rack whether they draw4 kW or 14 kW, and the elevation is identical either way.INFOThe declared mass is 217 kg of the 800 kg available (27%), leaving 583 kg.INFO25 of 42 units are free, and the tallest device that would still fit is 24U.OKAll 9 devices are mounted inside the rack and no two claim the same unit.

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title "Rack D4 — dense compute"
units 42
power 4000 W
weight 800 kg

device "ToR switch"       at 42 height 1 power 320 weight 9
device "Compute node 01"  at 40 height 2 power 620 weight 26
device "Compute node 02"  at 38 height 2 power 620 weight 26
device "Compute node 03"  at 36 height 2 power 620 weight 26
device "Compute node 04"  at 34 height 2 power 620 weight 26
device "Compute node 05"  at 32 height 2 power 620 weight 26
device "Compute node 06"  at 30 height 2 power 620 weight 26
device "Compute node 07"  at 28 height 2 power 620 weight 26
device "Compute node 08"  at 26 height 2 power 620 weight 26