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.

Question

Kendra Mayer

Mathematics

25 June, 10:01

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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Nicole Wyatt · 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.