Brain Teasers
Prewrapped Salad Free Kebabs
Mad Ade's Uncle Frenzied Fred owns a small prewrapped salad free kebab stand. When he places his prepackaged Kebabs on display he notices that he has 1 left over if he places them in groups of three. The same happens if he tries to place them in groups of 5, 7, or 9.
It is only when he places the kebabs in groups of 11 that all the kebabs are used.
How many prewrapped salad free Kebabs did Frenzied Fred have at least?
It is only when he places the kebabs in groups of 11 that all the kebabs are used.
How many prewrapped salad free Kebabs did Frenzied Fred have at least?
Answer
Assume the number of Kebabs is A. Then A-1 is divisible by 3, 5, 7 and 9. So, A-1 is a multiple of 5*7*9 = 315 (note: 9 is also a multiple of 3, so 3 must not be included!). We are looking for a value of N for which holds that 315*N + 1 is divisible by 11. After some trying it turns out that N = 3. This means that Mad Ade's uncle has 946 prewrapped salad free Kebabs.Hide Answer Show Answer
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