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# Problem of the Rabbits

A farmer owns a number of rabbits. If divided by 2, one rabbit remains.If divided by 3, 2 rabbits remain.If divided by 4, 3 rabbits remain.If divided by 5, 4 rabbits remain.If divided by 6, 5 rabbits remain.

How many rabbits does the farmer have ??

P.S : I know the answer but not the solution.

4 years, 7 months ago

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59.From the conditions we can find out that the answer is $$[2,3,4,5,6] -1$$ which is$$60-1=59$$

- 4 years, 7 months ago

What does [2,3,4,5,6] mean ?

- 4 years, 7 months ago

The LCM of those numbers...that's all.

- 4 years, 7 months ago

answer is 59. Since if it is divided by 2 we get remainder 1, it is odd. Combine this with the fact that when it is divided by 5 remainder 4, its last digit must be 9. After minus 1 out of multiples of 6, the numbers which have 9 as last digit are 29,59,89....And after minus 1 from multiples of 4, the numbers which have 9 as last digit are 19,39,59... Therefore, it is clear that the answer is 59.

- 4 years, 7 months ago

Thanks :)

- 4 years, 7 months ago

first do lcm of 2,3,4,5,6 its 60 as the remainder is 1 less than the divisor so the answer is 60-1=59

- 4 years, 7 months ago

This is simply a system of modular congruence.

- 4 years, 7 months ago