You've got a sack of corn, a chicken, and a fox. You have to cross a river, but you can only carry them one at a time. If you leave the chicken with the sack of corn, the chicken will eat the corn. If you leave the fox alone with the chicken, the fox will eat the bird.
How can you get all three things across the river safely?
Cross the river with the chicken, then go back and carry the corn over the river. However, instead of leaving the corn with the bird, return together with the chicken. Cross the river for the third time with the fox, leaving the chicken behind. Leave the fox with the sack of corn, and return for the last time to get the chicken. Done!
Mike has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
301 eggs.
The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1.
For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.
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