Guest Posted July 23, 2008 Report Share Posted July 23, 2008 A fruit seller has some number of apples and needs to divide them into equal groups. He divides them in groups of 2, but finds he has 1 left over. Then he divides in groups of 3, but has 2 left over. Then he divides in groups of 4, but has 3 left over. And so on, until he gets to dividing in groups of 17, and the apples fit perfectly. What is the minimum number of apples he has? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 SO SIMPLE ITS 119 AS WHEN DIVIDED BY 17 IT GIVES 7 MEANS EXACTLY DIV. WHEN DIVIDED BY 4 IT GIVES 3 REMAINING OUT WHEN DIVIDED BY 3 IT GIVES 2REMAINING OUT WHEN DIVIDED BY 2 IT GIVES 1REMAINING OUT SO IT'S 119 AT MINIMUM It's called SPOILER! Use it! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 A fruit seller has some number of apples and needs to divide them into equal groups. He divides them in groups of 2, but finds he has 1 left over. Then he divides in groups of 3, but has 2 left over. Then he divides in groups of 4, but has 3 left over. And so on, until he gets to dividing in groups of 17, and the apples fit perfectly. What is the minimum number of apples he has? 5045039 ... That is the minimum number of apples he had Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 119 without a doubt. Unless you intend for us to go beyond 4 to say 5 with 4 left over, 6 with 5 left over, etc. Can't be... the riddle says "and so on" so you have to use 5 with 4 left over, 6 with 5 left over, etc. until you get to 17. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 Yes, you get remainder of 1, which is what i mean - the question assume that we have spotted a pattern in the remainders. I was saying that he OP needs to hit that point home a bit more. If you're not smart enough to read "and so on" and figure out the pattern you're probably not smart enough to figure out the puzzle. It's called SPOILER! Use it! Not really a spoiler if he's wrong...which he is. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 If you're not smart enough to read "and so on" and figure out the pattern you're probably not smart enough to figure out the puzzle. Not really a spoiler if he's wrong...which he is. It's more the fact that, right or wrong, he should use a spoiler...Cause what if he WAS right...Then a spoiler should have been used. So either way...Use a spoiler. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 5045039 I noticed others came up with this as well. <_< I still don't know if it's the minimum. Has that question been answered? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 It's called SPOILER! Use it! He's called a NEWBIE!! He just joined anyways. Don't be too 'harsh'. lol Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 24, 2008 Report Share Posted July 24, 2008 I noticed others came up with this as well. <_< I still don't know if it's the minimum. Has that question been answered? 5045039 I came up with the same number, and went ahead to check... it is the Minimum. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 24, 2008 Report Share Posted July 24, 2008 Yes it is 5045039 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 24, 2008 Report Share Posted July 24, 2008 (edited) Yes it is 5045039 Ok, can you tell me how you derived this number ? Edited July 24, 2008 by Ben Law Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 24, 2008 Report Share Posted July 24, 2008 Ok, can you tell me how you derived this number ? The answer I got is 5045039 which I got the following way. Find the least common multiple of all numbers from 2 to 16 and subtract one from it. This number satisfies all the conditions of remainders for numbers 2 to 16. Now in order for the number to satisfy the condition of being divisible by 17, multiply the LCM by 2,3,4 etc and subtract one (these numbers also satisfy the remainders condition) till you find the one divisible by 17. Turns out, 720720 is the LCM and 720720*7-1 = 540539 satisfies all conditions. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 24, 2008 Report Share Posted July 24, 2008 saw the puzzle late.. but the soln is correct and also the methodology.. though there is one more method. extremely longer though... [spoiler='soln '] As it is divisible by 17, lets assume no 2 be 17x -also it leaves remainder as 9 after dividing it by 10, so last digit is 9 -it has remainder of 2 when divided by 3, so the series of no before 9 is 2,5,8,11...... 122........2103........504503.... -as multiple of 17, and we know its 7*7 which gives 9 as last digit, so no has to be either 27,37,47........... 296767... -similarly find series for all.. and after a few hours u will find soln..... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 24, 2008 Report Share Posted July 24, 2008 119 is the minimum number of apples that he will need to have with him A fruit seller has some number of apples and needs to divide them into equal groups. He divides them in groups of 2, but finds he has 1 left over. Then he divides in groups of 3, but has 2 left over. Then he divides in groups of 4, but has 3 left over. And so on, until he gets to dividing in groups of 17, and the apples fit perfectly. What is the minimum number of apples he has? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 24, 2008 Report Share Posted July 24, 2008 A fruit seller has some number of apples and needs to divide them into equal groups. He divides them in groups of 2, but finds he has 1 left over. Then he divides in groups of 3, but has 2 left over. Then he divides in groups of 4, but has 3 left over. And so on, until he gets to dividing in groups of 17, and the apples fit perfectly. What is the minimum number of apples he has? 5045039? Quote Link to comment Share on other sites More sharing options...
Question
Guest
A fruit seller has some number of apples and needs to divide them into equal groups.
He divides them in groups of 2, but finds he has 1 left over.
Then he divides in groups of 3, but has 2 left over.
Then he divides in groups of 4, but has 3 left over.
And so on, until he gets to dividing in groups of 17,
and the apples fit perfectly.
What is the minimum number of apples he has?
Link to comment
Share on other sites
39 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.