Ha ha! New puzzle! this one is hard.
Once upon a time, and old lady went to sell her vast quantity of eggs at the local market.
When asked how many she had, she replied:
Son, I can’t count past 100 but I know that.
If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be one egg left.
If you divide the number of eggs by 4 there will be one egg left.
If you divide the number of eggs by 5 there will be one egg left.
If you divide the number of eggs by 6 there will be one egg left.
If you divide the number of eggs by 7 there will be one egg left.
If you divide the number of eggs by 8 there will be one egg left.
If you divide the number of eggs by 9 there will be one egg left.
If you divide the number of eggs by 10 there will be one egg left.
Finally. If you divide the Number of eggs by 11 there will be NO EGGS left!
What is the minimum amount of eggs the old lady had?
Answer in the comments in 1 week. Put your answers in there beforehand and later comment on the puzzle.
A minimum of 25,201 eggs. This puzzle has a few different methods for finding the solution, one of which is:
Find a number into which all of the numbers from 2 to 10 divide evenly. You can do this by simply using 2*3*4*5*6*7*8*9*10, but you can find a smaller number by finding the prime factors, a subset of which can be used to form any number from 2 to 10. 2*2*2*3*3*5*7 will do. This comes out to be 2520, and is the lowest number into which all the numbers 2-10 divide evenly.
We can add 1 to this number to satisfy the first 9 constraints of the puzzle (the remainder of 2521/2, 2521/3 … 2521/10 is one), but this does not satisfy the last constraint, divisibility by 11.
Fortunately, we can multiply X (2520) by any integer and add 1 and we will still satisfy constraints 1-9. So what we do is multiply X by Y (variable integer) so that (X*Y) + 1 is divisible by 11. 1*2520/11 has a remainder of 1. So 2*2520 divided by eleven would have a remainder of 1+1 = 2, Now what we need is there to be a remainder of ten so we can add one and evenly divide by 11. 10*2520s divided by 11 would have a remainder of 10. 10*2520 equals 25200. That number plus one would be the number 25201. To check divide it by 2-10 and you should have a remainder of one, but it will divide by eleven evenly. therefore 25201 is the answer.
this puzzle came from brainbashers.com