Random problem I found.

[hello12223]

John has a list of integers which are all larger than 0 but less than 1000. He notices that every number in this list is either one third of another number in the list or three times another number in the list. What is the greatest number of different whole numbers which can be on John's list.

A friend of mine sent this question and I don't know where to start. Any help?

 

[Deleted member 4993]

John has a list of integers which are all larger than 0 but less than 1000. He notices that every number in this list is either one third of another number in the list or three times another number in the list. What is the greatest number of different whole numbers which can be on John's list.

A friend of mine sent this question and I don't know where to start. Any help?

You could definitely start with 1!

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this problem.

 

[hello12223]

Hello, after a bit of thinking, I decided to list as many consecutive integers from one so that each of them multiplied by three yields a result less than 1000. So I got 1-333 and each of these number's multiple of three. So is the answer 666?

 

[JayJay]

Hello, after a bit of thinking, I decided to list as many consecutive integers from one so that each of them multiplied by three yields a result less than 1000. So I got 1-333 and each of these number's multiple of three. So is the answer 666?

You have included some numbers twice. E.g. "3" was in your list of numbers that could be multiplied by three but also included because it is a multiple of three.