Puzzles by Amit Dudeja

  A man has 1000 bulbs in his house but only 10 switches . He wants to arrange the bulbs so that by flipping the switches in different ON/OFF combinations, he can light up any exact number of bulbs from 1 to 1000 . How should he distribute the bulbs among the 10 switches? 🧮 Step‑by‑Step Solution Key Idea: Binary Representation Each switch represents a binary digit (bit) . With 10 switches, there are 2 10 = 1024 possible ON/OFF combinations. That’s enough to represent all numbers from 0 to 1023 . Since we only need 1 to 1000 , this works perfectly. Distribution of Bulbs Assign bulbs to switches in powers of 2 : Switch 1 → controls 1 bulb Switch 2 → controls 2 bulbs Switch 3 → controls 4 bulbs Switch 4 → controls 8 bulbs Switch 5 → controls 16 bulbs Switch 6 → controls 32 bulbs Switch 7 → controls 64 bulbs Switch 8 → controls 128 bulbs Switch 9 → controls 256 bulbs Switch 10 → controls 489 bulbs (to make the total exactly 1000) Verification To light 1 bulb → turn ON switch 1. To...

  Problem Statement A man has a stick of 10 feet length . He cuts 1 foot daily from the stick. How many days will it take him to cut the stick completely into 1‑foot pieces? 🧮 Step‑by‑Step Solution The stick is 10 feet long . To make it into 1‑foot pieces , he needs to make 9 cuts (because after 9 cuts, the stick naturally becomes 10 separate 1‑foot pieces). Since he cuts 1 foot daily , it will take him 9 days to finish cutting the stick. ✅ Final Answer It will take the man 9 days to cut the 10‑foot stick into 1‑foot pieces.

   Problem Statement A cloth of 1 meter length and 1 meter width costs ₹100 . If you buy a cloth of ½ meter length and ½ meter width , how much should you pay? 🧮 Step‑by‑Step Solution Area of full cloth (1 m × 1 m): 1 × 1 = 1  square meter Cost = ₹100. Area of half cloth (0.5 m × 0.5 m): 0.5 × 0.5 = 0.25  square meter Cost per square meter: ₹ 100 1 = ₹ 100  per square meter Cost of 0.25 square meter: 100 × 0.25 = ₹ 25 ✅ Final Answer You have to pay ₹25 for a cloth of ½ meter length and ½ meter width .

  Problem Statement You have a total of 40 kg to divide into four measuring weights . The challenge: Choose the sizes of these four weights so that you can measure every integer weight from 1 kg to 40 kg using combinations of them. 🧮 Step‑by‑Step Solution This puzzle is solved using the binary system (powers of 2) . With 4 weights, the most efficient split is: 1 kg, 3 kg, 9 kg, and 27 kg . Their total = 1 + 3 + 9 + 27 = 40 . Using combinations of these, you can measure any number from 1 to 40 . Verification Examples 1 kg → directly with 1. 7 kg → 3 + 3 + 1 (or 9 − 2). 15 kg → 9 + 3 + 3. 28 kg → 27 + 1. 40 kg → 27 + 9 + 3 + 1. This works because each weight is roughly triple the previous one (balanced ternary logic), ensuring full coverage.

  Problem Statement A man cuts some flowers from a tree. He dips the flowers into the first well , and the flowers double . He donates a fixed number of flowers at the first temple . He dips the remaining flowers into the second well , and again the flowers double . He donates the same number of flowers at the second temple. He dips the remaining flowers into the third well , and once more the flowers double . He donates the same number of flowers at the third temple. After the third temple, he has no flowers left . Question: How many flowers did he originally cut from the tree? 🧮 Step‑by‑Step Solution Let the initial number of flowers = x . Let the fixed donation at each temple = d . At the First Well + Temple Flowers double → 2 x . He donates d . Remaining = 2 x − d . At the Second Well + Temple Flowers double → 2 ( 2 x − d ) = 4 x − 2 d . He donates d . Remaining = 4 x − 3 d . At the Third Well + Temple Flowers double → 2 ( 4 x − 3 d ) = 8 x − 6 d . He donates d . Remaining ...

  Problem Statement Two brothers have 8 kg of milk . They also have three measuring utensils with capacities of 8 kg, 5 kg, and 3 kg . Using only these utensils, how can they divide the milk into 4 kg each ? 🧮 Step‑by‑Step Solution Start: 8 kg of milk is in the 8 kg vessel . (8, 0, 0) Pour 5 kg into the 5 kg vessel . (3, 5, 0) Pour 3 kg from the 5 kg vessel into the 3 kg vessel . (3, 2, 3) Pour 3 kg from the 3 kg vessel back into the 8 kg vessel . (6, 2, 0) Pour 2 kg from the 5 kg vessel into the 3 kg vessel . (6, 0, 2) Pour 3 kg from the 8 kg vessel into the 5 kg vessel . (3, 3, 2) Pour 2 kg from the 3 kg vessel into the 5 kg vessel . (3, 5, 0) Pour 5 kg from the 5 kg vessel into the 8 kg vessel . (8, 0, 0) Now repeat the process to split into two equal 4 kg portions: Transfer 5 kg → (3, 5, 0) Transfer 3 kg → (3, 2, 3) Transfer 3 kg back → (6, 2, 0) Transfer 2 kg → (6, 0, 2) Transfer 2 kg into 8 kg vessel → (4, 0, 4) ✅ Final Answer The brothers can successfully di...