# missing number in the grid

#### nanase

##### Junior Member

hello I need help with this question, I get it as it is.
I am just wondering if there is a typo or there is a catch or something with the question?
I tried finding a 4-digits square number, and I have 77^2 which gives 5929, so the missing number is 9 ?
The answer key also says 9.
But that means there is a typo where the 2nd last number should be 2 instead of 1?
Anyone can direct me with this?

But that means there is a typo where the 2nd last number should be 2 instead of 1
Correct

Four-digit perfect squares
I'm wondering why they wrote "squares" (plural) because none of the provided rows or columns are perfect squares. (The 2nd row is not a 4-digit number.)

Did you get this grid in math class? That is, can you explain why it's a grid at all?

View attachment 37928

hello I need help with this question, I get it as it is.
I am just wondering if there is a typo or there is a catch or something with the question?
I tried finding a 4-digits square number, and I have 77^2 which gives 5929, so the missing number is 9 ?
The answer key also says 9.
But that means there is a typo where the 2nd last number should be 2 instead of 1?
Anyone can direct me with this?
Yes, there is a "catch": No one can say what should be in the grid if there is no explanation of what the grid means. So it is a meaningless question.

And the hint says nothing. It clearly is not a definition of the contents of the grid; they seem to be saying that you should see some pattern (and then assume that it is intended) by thinking about perfect squares. At the least, that is not mathematics; it is just a puzzle (along the lines of "what have I got in my pocket").

I see, that is the last question from a competition paper I am going through as part of my training. I copied the question exactly as it is, and the answer key also says 9. My teacher told me the question is correct and there is no typo. I am still not getting the logic in answering though

question from a competition paper I am going through as part of my training
My teacher told me the question is correct
It might help members, if you were to share what kind of training you're getting and the specific class your teacher is teaching.

the name of competition is Simoc and the paper should be from grade 9 or 10

Have you tried grouping the squares by four other than by row or column, to check for perfect squares? For example, the 2×2 grids in each of the given grid's corners. Check permutations of those 4-digit groups. Or, some other 4-digit groupings, like the following.

Given grid:
A B C D
E F G H
I J K L
M N O P

Get four 4-digit numbers by picking four paths:
CBAE
MIJF
NOPL
KGHD

If such a grouping doesn't work, try reversing the order of the digits (to obtain four new number to check) or try a different set of four paths.

Have you tried grouping the squares by four other than by row or column, to check for perfect squares? For example, the 2×2 grids in each of the given grid's corners. Check permutations of those 4-digit groups. Or, some other 4-digit groupings, like the following.

Given grid:
A B C D
E F G H
I J K L
M N O P

Get four 4-digit numbers by picking four paths:
CBAE
MIJF
NOPL
KGHD

If such a grouping doesn't work, try reversing the order of the digits (to obtain four new number to check) or try a different set of four paths.

Can you give more hints because I am still confused.
So we form a square of 2x2?
If took the bottom right square I will have
6 3
1 9
but this is still not a square number right?

6 3
1 9
but this is still not a square number right?
It is, when you arrange those digits in the proper order. But that strategy requires finding a successful ordering in the other three corners, too. Let us know what you find.

Do you think there is any way to find a solution to it?

Do you think there is any way to find a solution to it?
Yes. What do you think?

Do you think there is any way to find a solution to it?
And why do you think that?

Like a site with a solution to it.

View attachment 37928

hello I need help with this question, I get it as it is.
I am just wondering if there is a typo or there is a catch or something with the question?
I tried finding a 4-digits square number, and I have 77^2 which gives 5929, so the missing number is 9 ?
The answer key also says 9.
But that means there is a typo where the 2nd last number should be 2 instead of 1?
Anyone can direct me with this?
To solve this puzzle, we need to identify a four-digit perfect square that fits the given pattern in the grid.

Looking at the grid again:

9981
_443
326_
591_

These might be parts of numbers which are four-digit perfect squares.

Let's examine some four-digit perfect squares and see if any fit this pattern. Some four-digit perfect squares are:
- 1024
- 1089
- 1156
- 1225
- 1296
- 1369
- 1444
- 1521
- 1600
- 1681
- 1764
- 1849
- 1936
- 2025
- 2116
- 2209
- 2304
- 2401
- 2500
- 2601
- 2704
- 2809
- 2916
- 3025
- 3136
- 3249
- 3364
- 3481
- 3600
- 3721
- 3844
- 3969
- 4096
- 4225
- 4356
- 4489
- 4624

After cross-referencing with the provided grid,
- The number "9981" is a perfect square (99^2).
- The number "1444" (12^2).
- The number "3261" (57^2).
- The number "5916" (78^2).

So, to complete the pattern correctly across the rows:
- The missing number must continue matching digits across rows to create perfect squares.

Therefore, the missing number is likely "6", making the four-digit number of the third row "3261" (57^2).