+24 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?
+150 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.
+150 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.
+24 same lmao andddd your wronng
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 .
+746 PN that soluntion is for a different question. Anthrax is right.
