Elementary School Entrance Exam Question

[igorlord]

"What number does ? stand for on the last line?"
(taken from here)

8809 = 6
7111 = 0
2172 = 0
6666 = 4
1111 = 0
3213 = 0
7662 = 2
9312 = 1
0000 = 4
2222 = 0
3333 = 0
5555 = 0
8193 = 3
8096 = 5
7777 = 0
9999 = 4
7756 = 1
6855 = 3
9881 = 5
5531 = 0
2581 = ?

Hint (read ONLY if you are stuck!): An "average" preschooler will likely have a much easier time

Comments

[zachtogerasim]

statistically, it should be 2

[igorlord]

:) This is very interesting. Could you elaborate on the application of statistics to this problem? :)

[zachtogerasim]

among the answers, we have nine 0s, two 1s, one 2, two 3s, three 4s, two 5s and one 6
if you plot this, you will see that the only way to make the curve smoother is to answer 2 :-)

[igorlord]

Intriguing! What curve were you trying to fit over the data? Probably a picture of a "before" and "after" curve would serve as a decent illustration? :) :)

[alinaf]

2 :)

[syarzhuk]

Since counting holes is really adding ones, and they can "hardly even add"...
Again, I can write a 2 with two holes in it!

[igorlord]

:) There is a huge diference between counting and adding. Counting is just memorizing a sequence of words and naming the next word on a que. It has nothing to do with actually doing arithmetic.

You can count in fruits: "apple" "orange" "pear" "banana" "kiwi". But it makes little sense to say: "What do you get when you add an orange to a pear?"

Also, it does not really matter how one might draw "2". Neither it matters whether one can express 2 in binary or as a Roman numeral. The preschoolers are just given a picture, one concreete picture, just as the one above. Everything else (like diferent fonts or number systems) is just an adult/educated overcomplication of a simple problem. :) :)

[syarzhuk]

Counting is just memorizing a sequence of words and naming the next word on a que
Not necessarily, you're talking about simply saying the words "one, two, three, uno, dos, tres, apple, orange, pear". But there's more to it. There's a .GT./.LT. relationship between numbers, even a 3 year old kid can distinguish between one apple and two apples. So if you count in fruits, the answer to "What do you get when you add two apples?" is "an orange". Of course, this will require the understanding of the concept of an abstract number.

[igorlord]

.GT./.LT. relationship is actually much closer to counting than to arithmetics. It is simply a "goes before" relationship that does not need to have anything to do with other properties of a sequence or any of the properties of the elements in the sequence.

"kiwi" > "orange" simply means that "orange" goes before "kiwi".

Of course, if you ask a kid "Which jar has more candy?", the kid may well answer, but he would not be using arithmetic for that. He would be using some other heuristics (one that for descreet objects probably has some special cases for objects up to 6-8).

[pwaa]

So, did Gosha get it right?

[igorlord]

I did not test him, yet. I think he would not be able to do it. It does require counting at least to 6 (in the given example) and a bit of patience (the list is rather long). I think I might try it next year. After all, the test is for about 6-year-old, and Gosha is not even 3, yet.

[igorlord]

I.e. Gosha can count to about 15 now, but he certainly needs a lot of concentration for that, which is not compatible with doing it for a long list.

[angerona]

I think it's a horrible test (and I did solve it). we think it's "easy" because it doesn't involve multiplication, etc. But the point is that the kid is supposed to be able to understand sequences and be able to work through seemingly crazy attempts to figure out the one that's needed. Counting holes in numbers is not natural once a kid learns a number as a "number" not as "strange shape that has a circle in it." That's what human brain is all about -- learning and abstracting.

[igorlord]

I agree. It is a very tricky test.

It does use a number as a number on the right side, but as a pure picture on the left side.

A kid does not have to understand sequences here at all. He just needs to understand what the example means, while each example stands on its own (no sequences).

Still, kids are a lot less "burdened" with "additional complications" that adults try out before standing back and looking for a trivial solution.