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Pumpkin Purveyors is a puzzle in Professor Layton and the Azran Legacy.

Puzzle

Four sisters are taking the pumpkins they have grown to the market in the village. Each pumpkin weighs between one and 16 kilograms. Each sister carries 34 kilograms in total. A and C carry the same number of pumpkins, and B carries the most.

The sisters have all chosen some pumpkins they plan to carry, but how do the rest of them get shared out?

The numbers on the pumpkins indicate how many kilograms they weigh.

Hints




Click a Tab to reveal the Hint.

As a starting point, here's how much each sister is currently carrying:

A: 16 + 3 = 19 B: 4 + 2 + 6 = 12 C: 12 + 1 = 13 D: 11 + 8 = 19

Given that each sister carries 34 kilograms in total:

A can carry another 15 kilos. B can carry another 22 kilos. C can carry another 21 kilos. D can carry another 15 kilos.

How can you divide the pumpkins so that both A and D carry another 15 kilos?

We know that both A and C end up carrying the same number of pumpkins, so you know that the 15 kilograms of additional weight carried by A can't be made up by one 15-kilogram pumpkin.

Why? Because C needs at least two more pumpkins to make up the additional 21 kilos she has to carry.

Give A a five-kilo pumpkin and a ten-kilo one, then give D one weighing 15 kilos.

Give C a seven-kilo pumpkin and a 14-kilo pumpkin, then the answer should be right in front of you.


Solution

Incorrect

Too bad.

Are you sure the sisters each have a total of 34 kilograms in their baskets?

Correct

Smashing!

A carries pumpkins weighing three, five, ten, and 16 kilos. The pumpkins B carries weigh two, four, six, nine, and 13 kilos. C's basket holds pumpkins weighing one, seven, 12, and 14 kilos. D carries just three pumpkins, weighing eight, 11, and 15 kilos each.

If they don't sell them all, will they have to lug them back home again?

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