An Eggscellent Problem In Ginoni's farm shop, you can buy her freerange hens' eggs in boxes of 4, 6, 9 or 20. This means, for example, that you can have 21 eggs by buying two boxes of 6 and a box of 9. List the quantities of eggs that are impossible to buy from her shop. Ginoni notices that sales of the 4-egg boxes are poor, so discontinues that size. What is now the highest number of eggs that you can't buy? Prove that all larger quantities are possible.

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Mathematics

Stone

8 June, 22:59

An Eggscellent Problem In Ginoni's farm shop, you can buy her freerange hens' eggs in boxes of 4, 6, 9 or 20. This means, for example, that you can have 21 eggs by buying two boxes of 6 and a box of 9. List the quantities of eggs that are impossible to buy from her shop. Ginoni notices that sales of the 4-egg boxes are poor, so discontinues that size. What is now the highest number of eggs that you can't buy? Prove that all larger quantities are possible.

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Soren Maxwell · Answer 1

1,2,3,5,7,11 are quantities of eggs that cannot be bought when the box of 4 eggs is included. Without the box of 4 the highest number of eggs you can't buy is 43.