Welcome to Carsten's Test - Can You Solve the Equation?

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SUMMARY

The forum discussion centers around creating valid equations using the digits 0-9 with the insertion of plus signs and a single equals sign. Participants successfully identified multiple valid equations that equal 90, such as "1+2+3+4+56+7+8=90" and "12+3+45+6+7+8+9=90". Additionally, the conversation shifts to the concept of perfect numbers, with Njorl and Ben-CS discussing the definition and examples of perfect numbers, specifically 6 and 28.

PREREQUISITES
  • Understanding of basic arithmetic operations (addition and equality).
  • Familiarity with the concept of perfect numbers in number theory.
  • Knowledge of factors and their role in determining perfect numbers.
  • Basic problem-solving skills to formulate equations from given digits.
NEXT STEPS
  • Research the properties of perfect numbers and their significance in mathematics.
  • Explore combinatorial mathematics to understand how to generate equations from a set of digits.
  • Learn about prime numbers and their relationship with perfect numbers.
  • Investigate mathematical puzzles and challenges that involve number manipulation.
USEFUL FOR

Mathematicians, educators, students, and puzzle enthusiasts interested in number theory and mathematical problem-solving.

arcnets
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Hi, I'm the guy formerly known as carsten. This is just a test to see if everything works.
OK, you have the numbers
1 2 3 4 5 6 7 8 9 0.
You may insert some + signs and one = sign so to make a valid equation.
Like
12+34+5+6+78=90 (oops, false! )

Happy posting, and a big thanks to Greg who does a great job IMO.
 
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Easy ..
1+2+3+4+5+67+8=90 :smile:
 
Yes. There's more solutions. :wink:
 
1 + 2 + 3 + 4 + 56 + 7 + 8 + 9 = 90
12 + 3 + 45 + 6 + 7 + 8 + 9 = 90
 
You used the 9's twice drag.

12+3+4+56+7+8=90
1+23+45+6+7+8=90
nothing =890
nothing=7890
etc.

Njorl
 
If 2n-1 is prime, what can you say about (2n-1)*(2n-1)?

Njorl
 
Perfect!
 
Absolutely. I thought that would take longer.

Njorl
 
Originally posted by Ben-CS
Perfect!
What do you mean perfect?
 
  • #10
A perfect number is equal to the sum of its factors. For this purpose, 1 is considered a factor, but the number itself is not.

Factors of 6 are 1,2,3 1+2+3=6
Factors of 28 are 1,2,4,7,14 1+2+4+7+14=28

6 and 28 are perfect.

Njorl
 

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