Question

You need a code to open a safe at rsm that contains the best math problems! a computer generates five 6-digit numbers but only one of the numbers is the code. to identify it, you need to know that the sum of the digits in the ones place, hundreds place, and ten-thousands place is equal to the sum of the digits in the tens place, thousands place, and hundred- thousands place. can you identify the code even though some of the digits are missing?

Answer 1

To identify the code, we need to find a 6-digit number where the sum of certain digits is equal. Using placeholders, we can explore all possible combinations to determine the safe code.

Step-by-step explanation:

To identify the code, we need to find a 6-digit number where the sum of the digits in the ones place, hundreds place, and ten-thousands place is equal to the sum of the digits in the tens place, thousands place, and hundred-thousands place. Since some of the digits are missing, we can use placeholders to represent them. Let's say the code is ABCDEF, where A represents the thousands place, B represents the hundred-thousands place, and so on.

According to the given condition, A + C + E = B + D + F. Let's try different combinations of digits:

• If A = 1, then B + D + F = 1 + C + E.
• If A = 2, then B + D + F = 2 + C + E.
• If A = 3, then B + D + F = 3 + C + E.
• ...
• If A = 9, then B + D + F = 9 + C + E.

We can continue this pattern for each possible value of A. By trying all possible combinations, we can identify which 6-digit number satisfies the condition and find the code for the safe.