Forming a specific number with given numbers and operations

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SUMMARY

The discussion focuses on constructing an arithmetic expression R that equals a given natural number N using a specific set of natural numbers S and arithmetic operators. The problem is framed as a combinatorial challenge where each number in S must be used exactly once. A specific instance is provided with N = 24 and S = {1, 3, 4, 6}, where participants explore various combinations of the numbers and operators to achieve the target value.

PREREQUISITES
  • Understanding of basic arithmetic operations: addition, subtraction, multiplication, and division.
  • Familiarity with combinatorial problem-solving techniques.
  • Knowledge of natural numbers and their properties.
  • Ability to construct and evaluate mathematical expressions.
NEXT STEPS
  • Explore combinatorial algorithms for generating permutations of a set of numbers.
  • Learn about backtracking techniques for solving constraint satisfaction problems.
  • Investigate the use of recursive functions to evaluate arithmetic expressions dynamically.
  • Study mathematical optimization methods to minimize or maximize expressions under given constraints.
USEFUL FOR

Mathematicians, computer scientists, educators, and anyone interested in problem-solving with arithmetic expressions and combinatorial logic.

mah1
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Suppose you are given (1) a natural number N; (2) a set of natural num-
bers S = {n1; n2; : : : }; (3) a set of arithmetic operators, say +; -;*; =
(with the usual meaning of addition, multiplication, substraction, di-
vision). Your job is to construct an arithmetic expression R built from
the given operators and using each of the numbers in S exactly once,
with R = N.
(a) Explain in general how you could solve that problem.
(b) Solve the speci c instance: N = 24, S = {1; 3; 4; 6}
 
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so how would YOU do it?
 

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