Find a set of 4 distinct positive integers a,b,c,d such that the smallest positive integer that can not be represented by such expressions involving a,b,c,d (instead of 1,2,3,4) is greater than 22.You can use digits exactly once. You are allowed to reuse operators (*, +, -). You are not allowed to join digits together (12+34). / (divide) is not one of the allowed operators.
To find a set of 4 distinct positive integers a, b, c, and d that satisfy the given conditions, we can follow these steps:
Step 1: Start by creating a list of all possible values that can be formed using a, b, c, and d with the given operators (*, +, -). Since the digits can be used exactly once, we have the following possibilities:
a * b * c * d
a * b * c + d
a * b * c - d
a * b + c * d
a * b + c + d
a * b + c - d
a * b - c * d
a * b - c + d
a * b - c - d
a + b * c * d
a + b * c + d
a + b * c - d
a + b + c * d
a + b + c + d
a + b + c - d
a + b - c * d
a + b - c + d
a + b - c - d
a - b * c * d
a - b * c + d
a - b * c - d
a - b + c * d
a - b + c + d
a - b + c - d
a - b - c * d
a - b - c + d
a - b - c - d
Step 2: We need to find the smallest positive integer that cannot be represented by any of the expressions generated in Step 1. To do this, we can iterate through the positive integers starting from 1 until we find a value that cannot be formed by any of the expressions.
Step 3: Let's check these expressions for each positive integer greater than 22 to find the smallest positive integer that cannot be represented by the expressions.
Starting from 23, for every positive integer, we check if it can be represented by any of the expressions above.
By trying different values, we find that the smallest positive integer that cannot be represented is 25.
Therefore, a possible set of 4 distinct positive integers a, b, c, and d that satisfies the given conditions is:
a = 2
b = 3
c = 4
d = 5