Jump to content
BrainDen.com - Brain Teasers
  • 0


Guest
 Share

Question

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

Recommended Posts

  • 0

The fruit seller has a minimum of

323 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 17

Nothing like a good math problem to keep your brain in good shape.

Link to comment
Share on other sites

  • 0
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 17

Nothing 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

Link to comment
Share on other sites

  • 0

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... ?!?

Link to comment
Share on other sites

  • 0
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.

:(
Link to comment
Share on other sites

  • 0
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.

Link to comment
Share on other sites

  • 0
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.

Link to comment
Share on other sites

  • 0
[spoiler=This one fit, but not sure is the minimum :huh: ]

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.

Link to comment
Share on other sites

  • 0
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.

Link to comment
Share on other sites

  • 0
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 by rjsghk107
Link to comment
Share on other sites

  • 0
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!!

Link to comment
Share on other sites

  • 0

- 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?

Link to comment
Share on other sites

  • 0

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 by rjsghk107
Link to comment
Share on other sites

  • 0

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

Link to comment
Share on other sites

  • 0

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.

:blink:
Edited by Prince_Marth85
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...