Need help with math riddle

[TechBoyJK]

a farmer was on his way to the markey to sell some eggs when a neighbor boy on a motorbike accidentally knocked down the old man, causing him to break all the eggs in the wire basket he was carrying.

The scared boy was most apologetic fro the accident and said he would pay for the eggs.

He asked how many had been in the basket before the accident. . . .

the old man said "I don't know just how many I had. . but I did notice some patterns when I was cleaning them."

sets of 2 had 1 left over,
sets of 3 had one left over,
sets of four had one left over,
sets of 5 had one left over,
sets of six had one left over,
but sets of seven had none left over. . .

how many did he have?

 

[Zim Hosein]

27?

 

[Zalez]

1!

 

[TechBoyJK]

Originally posted by: Zim Hosein
27?

how?

 

[Zim Hosein]

Originally posted by: Zalez
1!

Really? Explain! &

 

[JeffCos]

has to be something high because no multiples of 7 minus 1 has 2,3,4,5 and 6 go into it evenly i'm up to 14x7

 

[YOyoYOhowsDAjello]

721?

EDIT:

7x103 = 721
6x120 = 720 + 1 left over
5x144 = 720 + 1 left over
4x180 = 720 + 1 left over
3x240 = 720 + 1 left over
2x360 = 720 + 1 left over

 

[KillerCharlie]

301
721
1141
1561
1981
2401
2821
3241
3661
4081
4501
4921

And so on... I only told Matlab to check up to 5000 though :thumbsup:

 

[JeffCos]

ok i looked on google, but i don't wanna ruin it for the people stull trying to figure it out....Jello you're too high

 

[KillerCharlie]

Originally posted by: JeffCos
Jello you're too high

No he's not.

 

[YOyoYOhowsDAjello]

Originally posted by: JeffCos
ok i looked on google, but i don't wanna ruin it for the people stull trying to figure it out....Jello you're too high

I think it solves it though, what's wrong?

 

[JeffCos]

well it's kinda of obvious they want the lowest one, so it's 301. So, YES, he is too high.

 

[YOyoYOhowsDAjello]

Originally posted by: JeffCos
well it's kinda of obvious they want the lowest one, so it's 301. So, YES, he is too high.

Where does it say that?

 

[Zim Hosein]

Argh!

 

[TechBoyJK]

Originally posted by: KillerCharlie
301
721
1141
1561
1981
2401
2821
3241
3661
4081
4501
4921

And so on... I only told Matlab to check up to 5000 though :thumbsup:

what is the logic... how is this number determined. is 301 the lowest number that will divide by 7 where the numerator isn't an increment of 1-2-3-4-5-6?

 

[YOyoYOhowsDAjello]

All I did was 6x5x4x3x2 = 720 then added 1 and it was divisible by 7 so I went with it.

I don't know the quick way to get 301 if that's the only right answer they're going to accept.

 

[KillerCharlie]

Originally posted by: YOyoYOhowsDAjello

Originally posted by: JeffCos
well it's kinda of obvious they want the lowest one, so it's 301. So, YES, he is too high.

Where does it say that?

Exactly...

I guess the real solution would be he had -119+j*420 eggs, where j is any integer greater than 0.

 

[imported_electron]

The answer is 32.

 

[YOyoYOhowsDAjello]

Originally posted by: KillerCharlie

Originally posted by: YOyoYOhowsDAjello

Originally posted by: JeffCos
well it's kinda of obvious they want the lowest one, so it's 301. So, YES, he is too high.

Where does it say that?

Exactly...

I guess the real solution would be he had -119+j*420 eggs, where j is any integer greater than 0.

That might even get you extra credit if you say that's the answer :thumbsup:

 

[KillerCharlie]

Originally posted by: TechBoyJK

Originally posted by: KillerCharlie
301
721
1141
1561
1981
2401
2821
3241
3661
4081
4501
4921

And so on... I only told Matlab to check up to 5000 though :thumbsup:

what is the logic... how is this number determined. is 301 the lowest number that will divide by 7 where the numerator isn't an increment of 1-2-3-4-5-6?

Logic? Pfft... who needs that when you can just write a program to do it. I know there is a way to do it mathematically, but since it has remainders it's probably abstract algebra or some crap like that.

 

[Howard]

1) number of eggs must be odd
6) number of eggs must be a multiple of 7, not violating above rule
4) number of eggs must be (a multiple of 5) + 1, not violating above rules
2) number of eggs must be (a multiple of 3) + 1, not violating above rules
3) number of eggs must be (a multiple of 4) + 1, not violating above rules
5) number of eggs must be (a multiple of 6) + 1, not violating above rules

Accordingly, the number must be an odd multiple of 7 whose last digit ends in either 1 or 6 (multiple of 5, plus 1).

91 is the first number, but does not satisfy rule 3)

161 is the next one, but does not satisfy rule 2) and possibly others
231 is the next one, but does not satisfy rule 2) and possibly others
301 is the next one, satisfies all rules

He had 301 eggs in the basket.

 

[TechBoyJK]

Originally posted by: KillerCharlie

Originally posted by: YOyoYOhowsDAjello

Originally posted by: JeffCos
well it's kinda of obvious they want the lowest one, so it's 301. So, YES, he is too high.

Where does it say that?

Exactly...

I guess the real solution would be he had -119+j*420 eggs, where j is any integer greater than 0.

someone is high, because 420 is now in the equation...

 

[YOyoYOhowsDAjello]

Originally posted by: TechBoyJK

Originally posted by: KillerCharlie

Originally posted by: YOyoYOhowsDAjello

Originally posted by: JeffCos
well it's kinda of obvious they want the lowest one, so it's 301. So, YES, he is too high.

Where does it say that?

Exactly...

I guess the real solution would be he had -119+j*420 eggs, where j is any integer greater than 0.

someone is high, because 420 is now in the equation...

Someone is high?

EDIT: oh...

 

[KillerCharlie]

So this old guy rearranges 300 eggs into groups of 2, 3, 4, 5, 6, and 7? I call bullcrap... he's just trying to get more money out of the biker dude.

 

[sao123]

4A + 1 = X
5B + 1 = X
6C + 1 = X
7D = X

God I hate simult equates