In the following question, select the missing number from the given series.
491691961728?100225144

Let's split the continuous string of numbers into distinct recognizable numbers:
The string can be written as blocks of three-digit and two-digit numbers:

49, 169, 196, 1728, ?, 100, 225, 144
Wait, let's observe the numbers carefully:

49=7
2


169=13
2


196=14
2


1728=12
3


100=10
2


225=15
2


144=12
2


Let's look for alternative groupings. Let's split it as a sequence of perfect squares or cubes:
4,9,16,91,96... No.

Let's group the digits into standard squares:

49=7
2


169=13
2


196=14
2


Let's look closely at the question string: 491691961728?100225144
Let's break it down into standard perfect squares:

49 (Square of 7)

169 (Square of 13)

196 (Square of 14)
Let's see the numbers at the end:

100 (Square of 10)

225 (Square of 15)

144 (Square of 12)

What about the middle part? 1728?
We know 1728=12
3
. What if the string is just a concatenation of perfect squares or mathematical relations?
Let's look at the squares of consecutive pairs or something similar.
Let's regroup the digits:
49,169,196,...
Let's check the base numbers: 7,13,14...

Let's try splitting the entire sequence into 2-digit or 3-digit numbers:
49,169,196,...
Wait! Let's see:
49→7
2

169→13
2

196→14
2

What if it's pairs?
49=7
2

169=13
2

196=14
2

What if it is a single sequence of bases:
Let's look at the alternatives: 27, 28, 26, 25.
If the missing item is a 2-digit number like 25, then the sequence contains:
49,169,196,1728,25,100,225,144
Let's list the roots/values:

49→7
2


169→13
2


196→14
2


1728→12
3


25→5
2


100→10
2


225→15
2


144→12
2


Let's look at the sequence of numbers if we split it differently:
4,9,16,9,1,9,6...
Let's test if it's squares of numbers:
2
2
=4
3
2
=9
4
2
=16
3
2
=9
1
2
=1
This doesn't seem uniform.

Let's rethink:
49
169
196
Notice that 169 and 196 are reverse of each other or related.
Look at the numbers at the end:
100,225,144.
144 is 12
2
. 225 is 15
2
.

Let's check if the digits are grouped as:
49=7
2

169=13
2

196=14
2

Then 17, 28? No, 1728 is a known cube (12
3
).
What if the question is composed of squares of numbers?
Let's look at the option 25: if the missing term is 25 (5
2
).
Let's look at option 27: if it is 27 (3
3
).

Let's check if it is a sequence of squares of some numbers:
Let's write down the sequence of squares:
7
2
=49
13
2
=169
14
2
=196
Then ?=25→5
2

Let's check if 1728 can be split as something else?
What if it's not 1728, but 17 is part of something else?
What if the sequence of squares is:
7
2
=49
4
2
=16
9
2
=81
Let's check the original string: 491691961728?100225144
Let's look at the numbers:
49,169,196,1728,25,100,225,144
Let's look at the roots: 7,13,14,12(cube),5,10,15,12.
Notice a pattern in the roots?
Let's look at groups of three:
Group 1: 49,169,196→7,13,14. Sum =7+13+14=34
Group 2: 100,225,144→10,15,12. Sum =10+15+12=37

Let's look at another elegant split:
49,16,91,96,17,28...
What if the numbers are squares of numbers in a certain order?
Let's look at the options: 27, 28, 26, 25.
If the answer is 25:
The sequence of numbers is:
49,169,196,1728,25,100,225,144
Wait! Let's check the squares of numbers from 7 onwards:
7
2
=49
8
2
=64
9
2
=81
10
2
=100
11
2
=121
12
2
=144
13
2
=169
14
2
=196
15
2
=225

Wow! Look at the squares present in the string:

49 (7
2
)

169 (13
2
)

196 (14
2
)

100 (10
2
)

225 (15
2
)

144 (12
2
)

What squares are missing from 7
2
to 15
2
?
The missing ones are 8
2
=64, 9
2
=81, 11
2
=121.
But we have 1728 in the middle. Let's see if 1728 contains roots or other numbers.
Wait, let's look at the remaining numbers if we remove the known squares:
If we take out 49,169,196, we are left with 1728?100225144.
We know 100,225,144 are 10
2
,15
2
,12
2
.
So the squares are: 7
2
,13
2
,14
2
and 10
2
,15
2
,12
2
.

Let's think if the series is just a list of squares of numbers:
Let's check the options: 25 is 5
2
.
If the answer is 25, then the sequence consists entirely of perfect squares (except 1728 if it's a cube, but 1728=12
3
).
Since 25 is the only perfect square among the options (27 is a cube, 26 and 28 are not powers), it fits perfectly into a sequence dominated by perfect squares.