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# AHHHHHELPPPP

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Lark has forgotten her locker combination. It is a sequence of three numbers, each in the range from 1 to 30, inclusive. She knows that the first number is odd, the second number is even, and the third number is a multiple of 3. How many combinations could possibly be Lark's?

May 3, 2019

#1
+3

AHHHHHHHOKAY

also what kinda name is Lark for a girl lmao

First number: within [1,30], there are 15 odd numbers.

Second number: within [1,30], there are 15 even numbers.

Third number: within [1,30], there are 10 numbers divisible by 3.

Therefore, \(15 * 15 * 10 = 2250\). There are 2250 possible combinations for Lark's locker.

May 3, 2019

#1
+3

AHHHHHHHOKAY

also what kinda name is Lark for a girl lmao

First number: within [1,30], there are 15 odd numbers.

Second number: within [1,30], there are 15 even numbers.

Third number: within [1,30], there are 10 numbers divisible by 3.

Therefore, \(15 * 15 * 10 = 2250\). There are 2250 possible combinations for Lark's locker.

Anthrax May 3, 2019
#2
-5

SOUTION

Let's try counting the number of perfect squares and cubes less than . There are twenty perfect squares less than 441: . There are also seven perfect cubes less than 441: . So there would seem to be 20+7=27 numbers less than 441 which are either perfect squares and perfect cubes.

But wait!  is both a perfect square and a perfect cube, so we've accidentally counted it twice. Similarly, we've counted any sixth power less than 441 twice because any sixth power is both a square and a cube at the same time. Fortunately, the only other such one is . Thus, there are 27-2=25 numbers less than 441 that are perfect squares or perfect cubes. Also, since  and , then all 25 of these numbers are no more than 400. To compensate for these twenty-five numbers missing from the list, we need to add the next twenty-five numbers: 401, 402, , 424, 425, none of which are perfect square or perfect cubes. Thus, the  term is .

ProffesorNobody  May 3, 2019
#3
+1

wait isn't that for a different question :(

Anthrax  May 3, 2019
#5
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PN that soluntion is for a different question. Anthrax is right.

ilovepuppies1880  May 3, 2019
#6
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c**p whoops ohh well. hes still wrong...

May 7, 2019