⚖️ Weighing ★★★★☆ +22 points #16

Four Weights for the Bazaar

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Open — answers are being collected The solution goes up on 07 September. Send in your answer before then and it counts for full points — you will not be told whether it is right until the reveal.

A trader at Chorsu bazaar has an old two-pan balance and wants to buy a set of four weights, so that he can weigh out any whole number of kilograms, starting from 1 kg, with no gaps.

The clever part: on a two-pan balance a weight may be placed on either pan. Put a weight next to the goods and it subtracts; put it on the far pan and it adds. With a 1 kg and a 3 kg weight he can already do 2 kg: goods + 1 on one side, 3 on the other.

3 − 1 = 2. A weight beside the goods works backwards.

⚖️Exactly four weights, each a whole number of kilos. Every whole weight from 1 kg upwards must be measurable — no gaps anywhere.

Find the four weights first. Then answer this:

Answer to type: the heaviest load, in kilograms, that the best set of four weights can measure.

💡 I want a nudge

Each weight can be on the far pan (+), beside the goods (−), or left in the box (0). Three choices per weight — where have you seen that before?

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