# 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

Instead of just stating the answer, I'll show a nice way to a approach unknown sequences, which is what you have until someone points out the obvious-once-you-know-it rule.First, a quick note about the 'it could be anything' answers. There is a truth here that is worth noting, but take care not to overdo it. If you're given the sequence 2, 4, 6, 8, ... and expected to continue it, only a deliberately tricksy question master would have in mind anything but the multiples of two (if I asked you to add some words to the list Iron, Lead, Tin,... you would be right to feel cheated if it turned out to be items on my kitchen table rather than metals or chemical elements). Be aware that some problems may yield a sequence that seems to be one thing when it isn't, but an unwritten assumption behind 99.9% of problems set by teachers is that there is a solution and it is, theoretically at least, within your grasp.So, unless you recognize the cube numbers - which you haven't if you're asking the question - how could you proceed?Look at the gaps. Linear sequences like 2n go up in regular steps, but quadratic sequences go up in steps that form a linear sequence themselves. Eg 1,4,9,16,25... goes up by 3, then 5, then 7, etc. So look at the gaps between the gaps. If it's still not clear, go back further. cubic sequences go up in quadratic steps, etc. You can even identify exponential sequences as the steps don't get simpler as you go further back.Now, your problem is a bit sneaky because you don’t have a very long string of numbers before a hole appears in the sequence, but you have a sequence of gaps that looks like: 7, 19, ?, ?, 91. If this sequence were going up in regular jumps, we would get 31 and 43 for the missing ones, and 55 instead of 91, so it’s not regular jumps.So far all this tells us is that the sequence is more complicated than a linear or quadratic sequence, but then the next simplest thing to check is cubic, which, for this sequence, is enough of a hint to make us consider cube numbers, and there’s your answer.Identifying the missing link from a messier cubic sequence would take a bit more work (I’d be tempted to hit it with some algebra, and I suspect it would involve solving quadratic equations because of the various unknowns).In general, the first few cube numbers, like the first few squares, are a handy type of number to recognise. They crop up all over the place.Finally, the answer should be 64. 4 times 4 times 4.

In the series shown below, which number does not fit in with the rest, 8, 27, 64, 100, 125, 216, and 343?

100 doesn't fit in this above series as all other numbers are cubes of successive natural numbers, starting right from 2.8=2^327=3^364=4^3and so on.