Highest number impossible to make with 6,9,20.

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In summary, the conversation is discussing the highest number that cannot be made by adding or using sums of the numbers 6, 9, or 20. The conversation suggests using mathematical methods such as McNugget numbers, Frobenius numbers, and the coin problem to solve this question. It is also suggested to use a computer program to generate numbers and look for a sequence of at least 6 consecutive numbers to find the answer.
  • #1
BR24
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What is the highest number you cannot make with the numbers 6, 9, or 20. Integers obviously. if you don't understand what i am asking, for example, you can't make 14, so which is the largest number you can't make since once you get so high you can make every number. Is there a quick or mathematical way to do this besides brute force and guessing?
 
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  • #2
cant eventually make every number, still looking for prime numbers, largest is 2^43,112,609 − 1 so far i think.
 
  • #3
dont think your right there, well don't think i stated the answer clear enough. you have to add, use their sums, not multiply. I know for a fact that the answer is below one million.
 
  • #4
Ah ok lol.
 
  • #5
yeah haha so any clue how to do it?
 
  • #6
can anyone confirm or disconfirm 43?
 
  • #7
BR24 said:
What is the highest number you cannot make with the numbers 6, 9, or 20. Integers obviously. if you don't understand what i am asking, for example, you can't make 14, so which is the largest number you can't make since once you get so high you can make every number. Is there a quick or mathematical way to do this besides brute force and guessing?
What do mean by "make"? Are you talking about adding them together or multiplying or some other combination of arithmetic operations?
 
  • #8
adding, corrected myself above.
 
  • #10
If you think it's under 1,000,000, just write a computer program to start generating numbers, sort the list, and look for a sequence of at least 6 consecutive numebrs. Clearly, you can make any number after that... since you just add 6 to one of those numbers.
 

What is the highest number that is impossible to make with 6, 9, and 20?

The highest number that is impossible to make with 6, 9, and 20 is 43.

Why is 43 the highest number impossible to make with 6, 9, and 20?

This is because 43 is the largest number that cannot be made by adding any combination of 6, 9, and 20 together. Any other number can be made by adding different combinations of these numbers.

How do you determine the highest number impossible to make with 6, 9, and 20?

To determine the highest number impossible to make with 6, 9, and 20, you need to use a mathematical concept called the "Frobenius number." This number is calculated by finding the greatest common divisor of the given numbers and subtracting it from their sum.

Can the highest number impossible to make with 6, 9, and 20 change?

No, the highest number impossible to make with 6, 9, and 20 will always be 43. This is because the numbers 6, 9, and 20 are relatively prime, meaning they do not have any common factors other than 1. Therefore, the Frobenius number will always be the same.

Can any other numbers be impossible to make with 6, 9, and 20?

Yes, any combination of numbers that are relatively prime can have a highest number that is impossible to make. It will depend on the specific numbers and their greatest common divisor.

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