Balance Scale Weighing Puzzle: How to Split 9 kg of Flour in Just 3 Weighings

This Week’s Daily Math Challenge

Here’s a puzzle to keep your brain sharp — perfect for winding down before bed.

You have a bag containing 9 kg of flour. What is the minimum number of weighings required to split the flour into two bags: one weighing 2 kg and one weighing 7 kg? You have a balance scale and two weights: 50 g and 200 g.

The Answer: 3 Weighings

Believe it or not, three weighings are all you need. Here’s how the balance scale weighing puzzle works step by step.

Weighing 1. Split the flour into two equal halves of 4.5 kg each. No weights are needed for this — simply distribute flour between both pans of the balance scale until they level out.

Weighing 2. Take one of the 4.5 kg portions and divide it in half again. You now have two portions of 2.25 kg each.

Weighing 3. Place one of the 2.25 kg portions on one pan. On the other pan, place both weights (50 g + 200 g = 250 g). Transfer flour from the 2.25 kg portion to the weights side until the scale balances. The flour remaining on the original pan is exactly 2 kg.

How the Balance Scale Weighing Puzzle Adds Up

At the end of three weighings, you have:

• 2 kg — the portion left after removing 250 g in the final step
• 7 kg — everything else combined: 4.5 kg + 2.25 kg + 0.25 kg = 7 kg

The total checks out: 2 + 7 = 9 kg.

Why This Puzzle Works

The elegance of this balance scale weighing puzzle lies in the halving strategy. By repeatedly bisecting the flour and then making a small precise correction using the weights, you reach the target amounts without any guesswork. The key insight is that 2.25 kg − 0.25 kg = 2 kg — a clean result hiding inside what looks like an awkward number.

Try sharing this one with a friend before giving away the answer. Most people assume it takes far more steps.