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.

#MathProblem

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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.

Rui-Xian Siew - 8 years, 2 months ago

Thanks :)

Ebrahiem Eladdad - 8 years, 2 months ago

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

Tan Li Xuan - 8 years, 2 months ago

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

Ebrahiem Eladdad - 8 years, 2 months ago

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

Rohan Rao - 8 years, 2 months ago

This is simply a system of modular congruence.

Alexander Sludds - 8 years, 2 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

Fatin Farhan - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$