This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the sum of the smallest and greatest numbers formed using the digits 6, 5, 9, and 3, with any digit repeating twice, we first need to understand what "repeating any digit twice" means. In this context, it means that one of the given digits will appear three times in the number, while the other three digits appear once. This will result in a 6-digit number (3 instances of the repeated digit + 3 distinct digits). The given digits are 3, 5, 6, 9. Step 1: Form the greatest 6-digit number. To form the greatest number, we want the largest digits in the highest place values. The largest digit available is 9. To make the number as large as possible, we repeat 9 twice, so it appears three times. The digits to use are 9, 9, 9, 6, 5, 3. Arranging these digits in descending order gives the greatest number: 999653 Step 2: Form the smallest 6-digit number. To form the smallest number, we want the smallest digits in the highest place values. The smallest digit available is 3. To make the number as small as possible, we repeat 3 twice, so it appears three times. The digits to use are 3, 3, 3, 5, 6, 9. Arranging these digits in ascending order gives the smallest number: 333569 Step 3: Calculate the sum of the greatest and smallest numbers. We add the two numbers found in Step 1 and Step 2. 999653 + 333569 999653 + 333569 = 1333222 The sum of the smallest and the greatest numbers is 1333222. That's 2 down. 3 left today — send the next one.