Can you solve the paper clip question for 2nd grade students?

The paper clip problem has stumped many adults after it was posted online. Can you figure it out?

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[Maussiegamer]

if someone says they had *some* donuts at home and they didnt have any donuts i would be pretty mad

[kerezol]

But it never said that Brian has boxes for all 10 or 100 paper clips. Just some. So the leftover can be a million, because he run out of boxes.

[BinderTh]

I think 301 is no solution. That means that Brian has no 10-clip-box, but the problem says "some boxes hold 10 clips", maybe even 412 is no solution, because 1 box is not "some boxes"...

[HenrySSJ]

-Hey bro, I'm Brian and I have some boxes that hold 10 paper clips.
-Cool, how many do u have?
-0

[hyperboloidofonesheet]

It is an ill-defined problem. A term like "some" must be defined; the idea of zero being "some" is counterintuitive, and even the idea of one being "some" is fuzzy. Additionally, it doesn't specify that leftover clips must be less than 10 or the number of 10-clip boxes must be less than 10. It is within the parameters of the problem that he has 473 leftover clips, thus 475 boxes of a hundred and 470 boxes of ten, and thus a total of 52, 673 paper clips.

[Ostap]

Not sure I understood which of the info claims that Brian has an empty box to put 10+ leftover clips into..

[yellstr]

By the same logic, where you derive that "some leftover clips" means "at least 1 leftover clip", "some boxes of 10 clips" means "at least 1 box of ten clips". So no, 301 is not a valid answer.

[CramcrumBrewbringer]

2:00 the question never specifies he has extra empty boxes.

[WRSomsky]

You're assuming that he is being efficient and every time he has sufficient clips he puts them in the bigger sized box. It would be best if the problem explicitly stated that.

[c.kevinchen]

This problem requires a couple of assumptions: a) Brian uses as many boxes of 100 as possible and as few loose paper clips as possible, and b) there's no limit to the boxes of 100 that Brian can have. I"m guessing that's what the main source of confusion is.

[redpug]

A better way to phrase it to clarify "leftover" means "couldn't fit in the box" would be:
Brian is filling paper clip boxes which contain either 100 or 10 paper clips each. After filling the boxes, he had some leftover that couldn't fill a whole box. ...

[trumpetbob]

This question is a far better predictor of being a future lawyer than a mathematician. Just reading through some of the comments already and I can see the loopholes in reasoning through the problem; this isn't a math puzzle but a wording one! I'll even add one more. Where does it say he actually FILLS the boxes? Sure, the box MAY hold 100 clips, but that box still holds 100 paperclips even if he only put 17 in there.

[RichardMellish]

We are told that he has "boxes" of 10 and of 100. If we take "boxes" literally, T must be at least 2.

[Mike-H_UK]

You could possibly reject 301 and 412 if you want to claim that 'boxes' is plural, so zero boxes or one box of any type does not work. Having said that, there is nothing in the question that limits the number of loose clips to 9 because 10 could be put into a box. Generally a poor question by an obviously poor teacher.

[paulsimpson]

Nowhere in the question does it state that if he has 10 individual paperclips, then he would put them in another box and have a box of 10, or that if he has 10 boxes of 10, then he would put them in a box of 100. He could, for example, have 20 boxes of 10, which would mean 23 boxes of 100 and 21 left over. As such there are an infinite number of solutions to this.
If, however, it had asked what the minimum number of clips were, then it depends on whether you consider zero as a valid instance of "some". If you do, then 301 is the minimum. If you don't then 412 is the minimum.

[TonyCAVR]

If you are thirsty and ask me for "some water" and I give you an empty bottle, you will still be thirsty.

[yurenchu]

From the thumbnail:
301 + 111k paperclips, for any positive integer k
where k is the number of 10-paperclips boxes.

[verkuilb]

At about 2:00, you make an assumption which isn't supported by the problem statement. You state that L must be less than 10, because if there were 10 or more, Brian would have put 10 of the left over clips into a box of 10. But that's not necessarily the case. The fact that Brian "has some boxes of paper clips", and that he "has some paper clips left over", doesn't in any way mean that he has less than ten left over. The way the problem is stated, he might not have enough empty boxes to hold all the left over paper clips. Or he might have plenty of empty boxes, but simply opted to not fill them all. So, for example, Brian could have 39 boxes of 100, 36 boxes of 10, and 37 leftover clips, for a total of 3900+360+37=4297 paper clips. THIS ANSWER FULFILLS THE PROBLEM STATEMENT!! In fact, any answer which fits the formula 190 + 111x (where x is any positive integer) is an acceptable answer!!

[richdobbs]

Nothing stops me from having 12 left over clips if some of the boxes have been damaged and thrown away. You didn't constrain the problem in the way you phrased it.

[jessewallis]

Some implies more than zero, boxes implies more than one… 523 is the least it could be.