Q1:ipmat indore 2021LRDI › WeightsEasySA · TITA

What is the minimum number of weights which enable us to weigh any integer number of grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only on the left pan)

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The Setup: We need to find the minimum number of weights to measure any integer from 1 to 100 grams. The catch? We can *only* place weights on the left pan. That means no subtractive combinations (like putting weights on both sides). We are strictly locked into binary combinations (base-2). Step 1: Understand the binary scale system. Since each weight can either be used (1) or not used (0), having $k$ weights can measure at most $2^k - 1$ distinct positive values. Step 2: Set up the inequality to cover everything up to 100 grams. $$2^k - 1 \ge 100$$ $$2^k \ge 101$$ Step 3: Find the smallest integer $k$ that satisfies this. We know our binary powers: * $2^6 = 64$ (too small) * $2^7 = 128$ (just right) Therefore, $k=7$ is the absolute minimum number of weights required. You'd literally just use the weights 1, 2, 4, 8, 16, 32, and 64 to carry the whole task. Final Answer: 7