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 He has minimum 720719 of apples Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 323 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 He has minimum 720719 of apples 720719 % 17 gives you 4 not 0. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 He has minimum 720719 of apples oops, mistake! Forget about my first answer. Let me calculate again....... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 323 323 % 5 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 323 % 5 [spoiler=This one fit, but not sure is the minimum ] 5045039 ? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 The fruit seller has a minimum of323 apples.Now how did I arrive there? I found what each 17%2 17%3 and 17%4 were, then created a simple chart and counted in base 2,3, and 4 at the same time until I had the correct remainder of each number. Turns out you need 19 groups of 17Nothing like a good math problem to keep your brain in good shape. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 The fruit seller has a minimum of I found what each 17%2 17%3 and 17%4 were, then created a simple chart and counted in base 2,3, and 4 at the same time until I had the correct remainder of each number. Turns out you need 19 groups of 17Nothing like a good math problem to keep your brain in good shape.323 apples.Now how did I arrive there? No Trader Sam 323 fails at 323 % 7 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 My guess is: 289 (?) Reason: its divisible by 17, so has to be a multiple of 17, but not divisible by 2,3,4,5 etc - so the first number that it could be is 17*17... ?!? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 My guess is: 289 (?) Reason: its divisible by 17, so has to be a multiple of 17, but not divisible by 2,3,4,5 etc - so the first number that it could be is 17*17... ?!? 289 does not satisfy any of the other conditions. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 289 does not satisfy any of the other conditions. OK, granted but I think you need to clarify that the remainder for all numbers less than 17 are one less than the number as 323 (as stated by other members) does fit your initial question. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 OK, granted but I think you need to clarify that the remainder for all numbers less than 17 are one less than the number as 323 (as stated by other members) does fit your initial question. Nope, it doesn't. Try to divide by 7 and see what you get. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 [spoiler=This one fit, but not sure is the minimum ] 5045039 ? The reason I choose this one because of 720720 is the lowest comman multiplier of 2, 3, 4, 5, 6, .... up to 16. So (720720- 1) is the first number which meet that when divided by number of x will left (x-1). HOWEVER this number doesn't meet the LAST condition, which, is can be divided fully by 17. So I try [(720720 x n) - 1] with n = 2, 3, 4, ... until I got the one which also meet the LAST condition which is 5045039. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 Nope, it doesn't. Try to divide by 7 and see what you get. 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 No Trader Sam 323 fails at 323 % 7 Yes It seems in my haste to solve I only read the first half of the question. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 119 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 (edited) 119 aw man. I got that answer, too. but u beat me to it. edit- but it turns out that we are wrong. 119 is divisible by 7 Edited July 23, 2008 by rjsghk107 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 aw man. I got that answer, too. but u beat me to it. edit- but it turns out that we are wrong. 119 is divisible by 7 Yep I know, but I got bored after 6 so stopped!! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 - It has to be a multiple of 17 because the number is divisible by 17 and 17 is a prime number. - The ones digit has a 9 because this number has a remainder of 9 after being divided by 10. - It is probably a prime number multiplied by 17 because the number isn't divisible by any of the numbers up to 17. Therefore, 17 times a prime number with a 7 in the ones digit. Am I right so far? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 (edited) the tens digit is probably 3, 7, 1, or 5 or not Edited July 23, 2008 by rjsghk107 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 (edited) 5045039 at least i THINK i got it. I didn't check. edit- i just realized that woon got my answer on the first page. -_-0 Edited July 23, 2008 by rjsghk107 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 i think there is no solution to this problem Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 119 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 23, 2008 Report Share Posted July 23, 2008 (edited) 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. Edited July 23, 2008 by Prince_Marth85 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.