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In 100 numbers you can select 50 all odd or 50 all even and there will be no consecutive pair. Picking another number must be of the opposite parity and so consecutive with one of your first 50.

Q: Show that if we select 51 distinct numbers from 1 to 100 at least two are consecutive numbers.?

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The least of the three numbers is 199.

Yes because at least one of the consecutive numbers will be even, and if you times anything by an even number, the answer will always be even

No. Any three consecutive numbers will have at least one of them which is divisible by 2, which means it cannot be prime. And since 1 is not considered a prime number, it cannot happen.

Zero. Any five consecutive natural numbers will contain at least one multiple of 2 and at least one multiple of 5, meaning that the product will be a multiple of 10.

Every sixth number will be a multiple of 6, so you need at least six consecutive numbers to guarantee that one of them will be divisible by 6.

Related questions

The least of the three numbers is 199.

No, because every other number in the number line is odd so therefore if you have any number of consecutive numbers you will have at least one odd number (if you're talking about consecutive numbers on a number line).

Yes because at least one of the consecutive numbers will be even, and if you times anything by an even number, the answer will always be even

No. Any three consecutive numbers will have at least one of them which is divisible by 2, which means it cannot be prime. And since 1 is not considered a prime number, it cannot happen.

Zero. Any five consecutive natural numbers will contain at least one multiple of 2 and at least one multiple of 5, meaning that the product will be a multiple of 10.

Every sixth number will be a multiple of 6, so you need at least six consecutive numbers to guarantee that one of them will be divisible by 6.

Consecutive numbers can't both be multiples of 7. The LCM of consecutive numbers is their product. 14 and 15 are consecutive numbers whose LCM is a multiple of 7 that is greater than 200.

Select ALL pairs of numbers that have a least common multiple of 30

A prime number is a whole number that has only two distinct factors: 1 and the number itself. A composite number has at least three distinct factors.

That is the median average!

3 consecutive numbers cannot be prime factors. Any three consecutive numbers would include at least one even number. The only even prime number is 2, and (2,3,4) doesn't qualify.

As the number 1 is considered a special case and not a prime, there cannot be three consecutive numbers that are prime. Any three consecutive numbers must include at least one even number. With the exception of the number 2, no even numbers are prime.