Are you smarter than a 4th grader? Solve the following problem?

[meetkitty123]

Can you answer this math assignment?

1) Draw the next pattern and 2) write down how many squares are in each.

3) what math pattern do you see?

4) How many squares would there be in step 7?

5) Can the #40 ever be an answer to one of the steps in this math pattern? Yes or no and 6) Why?

[abc3643]

Under the assumption that the pattern continues the squares outward with each level, then:

Let N = The level (aka the Step Number)

Let Q = The number of squares for that level.

The function is:

Q = 4N + 1

So,

For N = 1, then Q = 5
For N = 2, then Q = 9
For N = 3, then Q = 13
...
For N = 7, then Q = 29
For N = 8, then Q = 33
For N = 9, then Q = 37
For N = 10, then Q = 41

40 can never be an answer because of the extra square in the center that represents the 1 in Q = 4N + 1. Put another way, 40 mod 4 = 0 but Q mod 4 = 1 always. (That is, 40 is divisible by 4, but 4N + 1 is never divisible by 4 as it will leave a remainder of 1.

[abc3643]

We could also say "odd" and "even".
40 is even, Q will always be odd.

Mathematically, a number, Z, is:
even if Z mod 2 = 0
odd if Z mod 2 = 1

Well, for all integer values of N (the step), Q mod 2 = 1 yet 40 mod 2 = 0.

[WindAtMyBack]

There is no single correct answer to this. You could come up with several answers and justify them all.

That's the problem with these types of questions. They claim there is a correct answer when there is not. They often say that you should pick the most likely answer, which is basically admitting there is no single correct answer. Because what seems most likely to one person does not seem most likely to another person.

[WindAtMyBack]

I was just thinking about this question. For step 3 alone there are probably at least 20-30 answers, all of which can be justified. That means by steps 7 and 40, there is an astronomical number of possibilities.

People think in terms of squares. As a draftsman, I tend to think in terms of drawing it. The first step can be drawn with as little as 8 strokes. Step 2 requires 12 new strokes. So does step 3 require 12 new strokes? Does it require 16 new strokes (4 additional strokes each step). Or does it require 16 new strokes (50% more than the previous step).

I can also draw step one with 12 strokes. Which opens up a bunch of new possibilities.

I can also draw step one by drawing four squares. The fifth square is coincidental, since it depends on the placement of the four squares.

If I am allowed to retrace strokes, that opens up a bunch of other possibilities.

I can think of one other subtle pattern. Step 1 can be drawn without lifting your pencil, and without retracing existing lines. Step 2 can not. So does it alternate? This is actually a common type of question in math puzzle books.

[Julie_TS]

Using the very limited information here: 1&2. the next pattern would have 13 squares with one square added to each of the four legs of the pattern in step 2.

3. Starting with a base of 5, it appears adding 4 to the pattern every step.

4. Step 7 will have 29 squares.

5&6. 40 can never be the answer to any step. This due to the fact that we started with 5 and are adding a factor of 4 which will prevent us from ever reaching 40 exactly.

#Ineedahotbathafterallthat

[Julie_TS]

Thanks for the MHO!!!

[WhitneySnow]

No because the answer will never be an even number

[AI Opinion]

It appears you're working on a sequential pattern problem involving squares. To assist you, identifying the rule of progression is important. If a pattern of squares increases by a constant number every step, it indicates arithmetic progression. Thus, the expression for step 7 can be calculated by applying this rule. Without seeing the exact pattern, I can't specifically number the squares, but generally, utilize the sequence to predict step 7's outcome. As for 5, if you're referring to a specific number, it depends on whether it fits the established rule. Understanding this will clarify the progression logic.

[NathanDavis]

to the last question...

if you have the number 9, which is an odd number... and you keep adding four, four, four, which are even numbers... it would be fairly easy to say that the result will never be another even number, therefore the result would never be 40, only odd results

[AviatorTom]

There's insufficient information. Step 3 could be the same as step 1 (removing the added squares in step 2) or adding more squares (but where isn't specified) to the figure in step 2..

The only way to answer this question is to show what step 3 is, and then ask what is step 4?

[meetkitty123]

You have to count the squares.
Step 1 has 5 squares
Step 2 has 9 squares.
Following this pattern how many squares are in step 3?

[AviatorTom]

@meetkitty123 I cannot answer that with any certainty. The next square could have 5 squares, with overall sequence being 5-9-5-9-5-9... Or it could be 13 squares (4 more, but don't know they are placed). Or, it could be 17 squares (rule: double the previous number and subtract 1, eg 5*2-1=9, 9*2-1=17, with the next in sequence being 17*2-1=33 ...) still not knowing where they would be placed. And there are other possible sequences, possibly based on the position of each number in the sequence.

[IslaTheWitch]

there is missing information...

in the first pattern, in the middle is a square? or an empty place?

there are plenty of possible solutions if there are no other conditions...

[Lynx122]

You just add 4 at the ends in every step right? so it's 5,9,13,17,21,25,29,33,37,41

So 40 is not one of the answers. The question is not written very clearly though so I don't know if I understood it all the way it was meant.

[exitseven]

it is 13. Each step is incremented by 4. Step 7 would have 29 squares. 40 cannot ever be an answer

[lightbulb27]

Probably not,

3: a plus sign, or the cross.

4: 13

5: no

[Still-alive]

[fish5505_87]

I came here for recreation!

[shortster]

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13 squares. 19 squares. No, there will always be an odd number of squares; as we started with an odd number and always add an even number.

[shortster]

Darn, all my spaces disappeared. It was supposed to be a cross design.

[DrPepper12]

Sure. "ChatGPT what's the answer?"

[andreasderjuengere]

Nothing of these scribblings is resembling a proper square.

Yes - I am :)

[Anonymous]

squares = 4(step - 1) + 5

step7 has 29 squares

step9 has 37, step10 has 41. There isn't a step that has 40 squares.

[Opinion Owner]

Even better... 4 times any number is always even. Add an odd number like 5 and the result is always odd. So, there can never be a step that results in 40 squares.

[abc3643]

You wrote:
"squares = 4(step - 1) + 5"
which, when simplified, is:
squares = 4 * step - 4 + 5 = 4 * step + 1

[Opinion Owner]

@abc3643 True, that. My intent was clarity.

[Samantha_17]

4th graders are apparently smarter than me :)

[nawtee_me]

Add four squares with each turn and you get.
# Of squares 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49…

[TallAnon]

(4*X) 1
(4*7) 1
40 can not be the answer since 40-1 does not divide to a round number when divided by 4

[TallAnon]

Gag removed the plus sign 🤣

[larry69]

I am good at math and this confuses this 55 year old

[lorenzomichael]

I’m smarter than everybody because I’m the only one that understands that 1+1 is 11.

[OlderAndWiser]

N = (Step# X 2) + 1

[faith_it]

I'm not smart in academics

[Grond21]

1. 5
2. 9
3. 13
4. No.

[Uglygaypoorcoward94]

I have no clue

[PeterLegg91]

Probably not, kids are fricking clever these days

[Kelly6]

In step7, 25 squares

[PaleDale]

I'll leave this one to my friend's kid 😉

[Alexa6]

Something s sure not on everything.