Question

Prove that it is impossible to get the answer 1000 by using numbers 1-9 Only ONCE in three digit numbers

_ _ _ + _ _ _ + _ _ _
1, 2, 3, 4, 5, 6, 7, 8, 9

Answer 1

It is mathematically impossible to obtain the sum of 1000 using the numbers 1-9 only once in a three-digit addition due to the constraint of the fixed set of digits. The highest achievable sum under these conditions is 45.

Step-by-step explanation:

To explore this, let's consider the average of the digits 1-9: (1+2+3+4+5+6+7+8+9)/9 = 5. The sum of three three-digit numbers, each using these digits exactly once, would be three times this average, which is 3 * 5 = 15.

Therefore, the highest possible sum achievable with the numbers 1-9 only once in a three-digit addition is 15 * 3 = 45. Since 45 is significantly less than 1000, it is mathematically impossible to reach the desired sum of 1000 using the given set of numbers and constraints.

This limitation arises from the fixed values of the digits and the constraint of using each digit only once, preventing the combination of numbers needed to achieve a sum as high as 1000.