# Find The Odd Man Out 8 27 64 100 125 216 343

Find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer?

31² = 961
32² = 1024

9³ = 729
10³ = 1000

It comes down to the number of terms in the sequence 1², 2², 3², ... 31² plus the number of terms in the sequence 1³, 2³, 3³, ... 9³, taking into account those integers that are both squares and cubes.

1³ = 1 = 1²
4³ = 64 = 8²
9³ = 729 = 27²

31 + 9 - 3 = 37

I'm hoping (it's late a night!) that there are 37 positive integers fitting the given criteria.

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Find the odd man out 8,27,64,100,125,216,343?

100 is not a cube

1, 8, 9, 64, __, 216, 49, 512. What is the missing term?

The sequence is formed by using two rules:Two rules are as follows:Rule 1: Square the numbers at odd position.For example:[math]{1^2} = 1[/math][math]{3^2} = 9[/math][math]{5^2} = 25[/math]Rule 2: Cube the numbers at even position[math]{2^3} = 8[/math][math]{4^3} = 64[/math][math]{6^3} = 216[/math]Therefore,[math]{1^2},{2^3},{3^2},{4^3},{5^2},{6^3},{7^2},{8^3},{9^2}[/math]Missing term is [math]{5^2} = 25[/math].

The missing numbers in the below series would be 1:1, 8:4, 9:27, 64:16, 25:125, ?:?, 49:343?

216:36

each numbered pair is associated with 1,2,3,4,etc. one of the numbers is that number squared(nsquared). the other number is nsquared*n again). the numbers rotate so that the first number of the set is nsquared, then on the next set, n squared is the second number. they flip flop every other set.

How many integers in the range 1 to 1000 are perfect squares but not perfect cubes?

These are the perfect sqaures between 1 and 1000:

1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729
784
841
900
961

And these are the perfect cubes between 1 and 1000:

1
8
27
64
125
216
343
512
729
1000

It looks like 1, 64, and 729 appear in both lists, so you should remove these from the squares list to get your answer.

What is the missing number in the sequence shown below? 1 - 8 - 27 - ? - 125 - 216