In the game show, 'Who wants to be a millionaire', Aarrushi has reached into the last stage of the game where she is required to answer a question that will make her win 1 million pounds. Akhil, the host of the show asks the following question to her, 'I can give you money in orders of 6, 9 and 20 pounds. What is the largest amount of money I cannot give you?'What should be Aarrushi's answer so as to be declared the winner of the show?
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Answer: 43.
After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).
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