Question 150876This question is from textbook
: A woman with a basket of eggs finds that if she removes the eggs from the basket 2,3,4,5 or 6 at a time, there is always 1 egg left. However, if she removes the eggs 7 at a time, there are no eggs left. If the basket holds up to 500 eggs, how many eggs does the woman have?
This question is from textbook
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! You need to think this one through before trying some potential solutions
1) You need to realize that the answer must not be a number that is divisible by 2,3,4,5,6 -- so you immediately start thinking "prime numbers" greater than 7 are good candidates to try
2) In order for the 'solution' to leave a remainder of 1 when divided by 5, the solution must end in either a 1 or a 6.
3) A solution that ends in 6 won't work, since that solution fails when dividing by 2
So we need to multiply 7 by a number that results in a solution that ends in a 1. The only was that can happen is if the number we multiply by ends in a 3. (since 3 * 7 ends in a 1)
So, we are looking for a prime number that ends in 3.
Now comes the trial and error
try 13, 23, 43, 53 ...
13*7 = 91
works for 2, works for 3. fails for 4 since there are 3 eggs left
try 23
23*7 = 161
works for 2, fails for 3 with 2 eggs left
try 43
43*7 = 301
works for 2, 3, 4, 5, 6 tada!
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