The Man, the Wells, and the Flowers: A Doubling Donation Riddle

 

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 → 2x.

  • He donates d.

  • Remaining = 2x−d.

At the Second Well + Temple

  • Flowers double → 2(2x−d)=4x−2d.

  • He donates d.

  • Remaining = 4x−3d.

At the Third Well + Temple

  • Flowers double → 2(4x−3d)=8x−6d.

  • He donates d.

  • Remaining = 8x−7d.

Condition: After third temple, remaining = 0.

8x−7d=0
8x=7d
x=7d8

✅ Final Answer

The man originally had 78 of the flowers he donated each time.

For example:

  • If he donates 8 flowers each time (d=8), then initial flowers = 7.

  • If he donates 16 flowers each time (d=16), then initial flowers = 14.

Comments

Post a Comment

Popular posts from this blog

Four Weights to Measure Any Amount from 1 to 40 kg

  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.
Read more

The Stick Cutting Puzzle

  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.
Read more

The Cost of Half‑Sized Cloth

   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 .
Read more