Help me if youre good with math word problems

[wfbberzerker]

ok, i have this math problem that kind of has me stumped, and i'm wondering if you guys with your superior intellect can help me.
here goes:

the integers from 1 to 1000 are written in order around a circle. starting at 1, every 15th number is marked (i.e. 1, 16, 31...) but not removed. this is continued until all numbers that can be marked have been. how many unmarked numbers remain?


thanks for your help

 

[SHoddyCOmp]

Goodgoing, smarty.
lol

 

[wfbberzerker]

Originally posted by: SHoddyCOmp
Goodgoing, smarty.
lol

hardy har har. its fixed now

 

[Dragoon42]

gonna guess 944 unmarked numbers

 

[McPhreak]

it's late, but my guess is 800 unmarked give or take a couple

after you go around once, the first number you land on is 6
go around again, it's 11
go around again, it's 16 which is the second number you land on the first turn

Therefore, 3 turns of the wheel going 15 at a time
1000/15 = 66 2/3

multiply it by 3 and you get 200 marked = 800 unmarked.

 

[SHoddyCOmp]

so uhm, im probably wrong because i dont exactly understand it because it looks kinda simple but im being dumb tonight....uhhhh

1 is already marked to take that from 1000
999/15 = 66.6..... (66)numbers marked so that would leave 999-66=933 unmarked? Seems to simple to be that though ? confused

 

[SHoddyCOmp]

nice, 3 different answers, pick one
which makes sense more? I just divided by 15 by the remaining 999 (becauseif i did it by 1000 it would skip the one that was in the beginning which must have some significance) to find the number marked, it would almost be 67 but not quite in the 999 left....thats how i figured it anyway

 

[Dragoon42]

actually if the first number after you land on again is 6, 800 might be right, well unless your going to hit the same number again anytime soon

66x3 = 198 so 802 i think

 

[wfbberzerker]

Originally posted by: Dragoon42
err mistype in mine, i got with the 933 answer

i don't get why you go around 3x? i'm missing it here

you go around three times because after the third time around you hit 16, which you hit on the 1st time around (which means youre just repeating the same numbers from then on).

 

[McPhreak]

Originally posted by: Dragoon42
err mistype in mine, i got with the 933 answer

i don't get why you go around 3x? i'm missing it here

The word problem is basically saying if we have this wheel going from 1 to 1000 and start counting by 15s starting from one and you went around and around a gazillion times, are there any nunmbers on that wheel you wouldn't land on? That's why you need to go around more than once because after your first trip around, the first number you will hit will be 6 (1005 +1). Since you didn't land on 6 the first time you went around, you need to count this number and all the other numbers going around the second time....and thrid time...but on the fourth time around, the numbers you land on will be the same as those the very first time you went around (i.e 16, 31, 46, etc.).

 

[Insomnium]

1000 - 67 = 933 unmarked me thinks.

 

[SHoddyCOmp]

Originally posted by: McPhreak
it's late, but my guess is 800 unmarked give or take a couple

after you go around once, the first number you land on is 6
go around again, it's 11
go around again, it's 16 which is the second number you land on the first turn

Therefore, 3 turns of the wheel going 15 at a time
1000/15 = 66 2/3

multiply it by 3 and you get 200 marked = 800 unmarked.

huh!? im looking at it like every few degrees a number is marked. at 0/360 1 is, at every ~2.27 degrees another number is marked, which is 16, at the next degree just past 5, 31 is and so on. No different than on a number line i suppose just in a circular pattern which is meant to throw you off?

Interpretation

 

[SHoddyCOmp]

Originally posted by: Insomnium
1000 - 67 = 933 unmarked me thinks.

someone agrees with me!
Actually i should be doing my math hw myself right now, easy stuff though, blah sin and tan graphs

 

[McPhreak]

Originally posted by: SHoddyCOmp

Originally posted by: McPhreak
it's late, but my guess is 800 unmarked give or take a couple

after you go around once, the first number you land on is 6
go around again, it's 11
go around again, it's 16 which is the second number you land on the first turn

Therefore, 3 turns of the wheel going 15 at a time
1000/15 = 66 2/3

multiply it by 3 and you get 200 marked = 800 unmarked.

huh!? im looking at it like every few degrees a number is marked. at 0/360 1 is, at every ~2.27 degrees another number is marked, which is 16, at the next degree just past 5, 31 is and so on. No different than on a number line i suppose just in a circular pattern which is meant to throw you off?

Interpretation

Try the same problem except with a clock...start with 1-o'clock on a standard clock and count around by 5's until you start repeating and tell me what you get...

1,6,11,4,9,1,6,11,4,9...

The answer in this case is 7 unmarked, not 9.

 

[Insomnium]

933 unmarked from 1 to 1000 that is. Here's a program that proves this:

int counter = 0;

for(int k = 1; k <= 1000; k +=15)
{
System.out.println(k);
counter++;
}

Ya get 67 for counter. Damn, maybe i should stop procrastinating and do my homework

If you make it go up to 3000 and just disregard the thousands place and compare which ones repeat you should get the answer, but i dont really feel like coding that now.

(edit) errr nevermind its easier than i thought or perhaps I'm wrong, but there are exactly 200 numbers that are marked when you go around 3 times as was mentioned before.

 

[McPhreak]

Originally posted by: Insomnium
933 unmarked from 1 to 1000 that is. Here's a program that proves this:

int counter = 0;

for(int k = 1; k <= 1000; k +=15)
{
System.out.println(k);
counter++;
}

Ya get 67 for counter. Damn, maybe i should stop procrastinating and do my homework

I don't think you guys understand the question. Theres a reason why wtfberzerker mentioned that the numbers are written in order around a circle and that's so that you can continue counting after you've hit 991 (the last number you hit the first time around. What comes after 991 in the circle?

6

 

[Insomnium]

Originally posted by: McPhreak

Originally posted by: Insomnium
933 unmarked from 1 to 1000 that is. Here's a program that proves this:

int counter = 0;

for(int k = 1; k <= 1000; k +=15)
{
System.out.println(k);
counter++;
}

Ya get 67 for counter. Damn, maybe i should stop procrastinating and do my homework

I don't think you guys understand the question. Theres a reason why wtfberzerker mentioned that the numbers are written in order around a circle and that's so that you can continue counting after you've hit 991 (the last number you hit the first time around. What comes after 991 in the circle?

6

In which case you get 200 marked if you go around 3 times (see my edit above). Now do you have to take out ones that repeat? do some of them repeat?

 

[McPhreak]

Originally posted by: Insomnium

Originally posted by: McPhreak

Originally posted by: Insomnium
933 unmarked from 1 to 1000 that is. Here's a program that proves this:

int counter = 0;

for(int k = 1; k <= 1000; k +=15)
{
System.out.println(k);
counter++;
}

Ya get 67 for counter. Damn, maybe i should stop procrastinating and do my homework

I don't think you guys understand the question. Theres a reason why wtfberzerker mentioned that the numbers are written in order around a circle and that's so that you can continue counting after you've hit 991 (the last number you hit the first time around. What comes after 991 in the circle?

6

In which case you get 200 marked if you go around 3 times (see my edit above). Now do you have to take out ones that repeat? do some of them repeat?

no

 

[Moonbeam]

Seems like you would get 10X more than if you did it to a hundred.

1 16 31 46 61 76 91
6 21 36 51 66 81 96
11 26 41 56 71 86

Or 20 numbers so 200 for a thousand, as stated similarly.

 

[wfbberzerker]

hmm... i did some basic calculations myself, and i got around 200 marked, i think. it goes something like this:

the first time around, on the 67th mark, you are at 991 (it is 66 2/3 to get to 1000, basically 66 gets you to 991, but you have to include the 1 which you started on). the 68th mark, youre at 1006. another 66, and you get to 1996 (minus 1000). that makes it your 144th mark. on the 145th mark, youre at 2011 (minus 2000). add another 66 sets of 15, and you get to 3001 (minus 3001). so, i think that on your 210th mark, youre back at 1. hmm... or should it be 200th mark?

im not sure here...

 

[McPhreak]

Originally posted by: wfbberzerker
hmm... i did some basic calculations myself, and i got around 200 marked, i think. it goes something like this:

the first time around, on the 67th mark, you are at 991 (it is 66 2/3 to get to 1000, basically 66 gets you to 991, but you have to include the 1 which you started on). the 68th mark, youre at 1006. another 66, and you get to 1996 (minus 1000). that makes it your 144th mark. on the 145th mark, youre at 2011 (minus 2000). add another 66 sets of 15, and you get to 3001 (minus 3001). so, i think that on your 210th mark, youre back at 1. hmm... or should it be 200th mark?

im not sure here...

It's DEFINITELY not 210. I'm 99% sure it's 200, 1% sure it's 199 or 201

 

[silverpig]

Originally posted by: McPhreak

Originally posted by: Insomnium

Originally posted by: McPhreak

Originally posted by: Insomnium
933 unmarked from 1 to 1000 that is. Here's a program that proves this:

int counter = 0;

for(int k = 1; k <= 1000; k +=15)
{
System.out.println(k);
counter++;
}

Ya get 67 for counter. Damn, maybe i should stop procrastinating and do my homework

I don't think you guys understand the question. Theres a reason why wtfberzerker mentioned that the numbers are written in order around a circle and that's so that you can continue counting after you've hit 991 (the last number you hit the first time around. What comes after 991 in the circle?

6

In which case you get 200 marked if you go around 3 times (see my edit above). Now do you have to take out ones that repeat? do some of them repeat?

no

Enjoying your conversation with the collective wall that is this thread?

 

[wfbberzerker]

i got it!
i think did the problem right (when i wrote it all out) except for a little bit of addition.

lets copy and paste....
the first time around, on the 67th mark, you are at 991 (it is 66 2/3 to get to 1000, basically 66 gets you to 991, but you have to include the 1 which you started on). the 68th mark, youre at 1006. another 66, and you get to 1996 (minus 1000). that makes it your 134th mark. on the 145th mark, youre at 2011 (minus 2000). add another 66 sets of 15, and you get to 3001 (minus 3000). so, i think that on your 200th mark, you get back to 1.

i think this is the right answer.

 

[Insomnium]

I say 200 marked along with McPhreak; 99.9% sure that's what it is.

 

[silverpig]

It is 200 marks, so 800 unmarked.

In the first revolution the first mark is at 1, and the 67th mark is at 991. 990/15 = 66 but you have to add 1 because of you starting at 1, so that puts you at the 991st spot. Since that is the 66th number you jump to, you have to add one to your total marks because you started on 1, a marked number.

After 1 revolution you are at 991, with 67 marks.

The next revolution will bring you to 6 (991 + 15 = 1006 -> - 1000 -> 6). If you subtract 5, you will have the exact same loop as you just performed. 67 marks ending at 991. You then add 5 to find your ending spot again. 991 + 5 = 996 with 67 jumps.

After 2 revolutions you are at 996 with 67 + 67 = 134 marks.

The next revolution will bring you to 11 (996 + 15 = 1011 -> - 1000 -> 11). If you subtract 10, you will get the first loop over again. 67 marks ending at 991. Add 10 to find your ending spot. 991 + 10 = 1001. Now, this corresponds to place 1 which has already been marked in the very first revolution. Since this is the 67th mark of the third revolution and it has already been counted, that leaves us with 66 unique marks.

After 3 revolutions you are back at 1 with 134 + 66 = 200 marks.


This process will repeat itself, thus leaving you with 200 unique marks. 1000 number - 200 marked numbers = 800 unmarked numbers.