In a 4 digit number, the two greatest place-value digits are 2. The sum of the ones and tens digits is 14. What numbers are possible?

2295, 2259, 2286, 2277....

To solve this problem, let's take it step by step:

Step 1: Identify the given information.
- The two greatest place-value digits are 2.
- The sum of the ones and tens digits is 14.

Step 2: Determine the possible values for the thousands and hundreds digits.
Since the two greatest place-value digits are 2, the thousands and hundreds digits can each be either 0 or 2.

Step 3: Determine the possible values for the ones and tens digits.
Since the sum of the ones and tens digits is 14, and the two greatest place-value digits are 2, the only possible combination is 4 and 10. Therefore, the ones digit is 4 and the tens digit is 10 - 4 = 6.

Step 4: Combine the digits to form the possible numbers.
Based on the above deductions, we have the following two possible 4-digit numbers:
1. 2064
2. 2464

Therefore, the possible numbers are 2064 and 2464.

To find the possible numbers, we need to consider the given conditions. Let's break down the problem step by step:

Step 1: Identify the greatest place-value digits
The problem states that the two greatest place-value digits are 2. Therefore, the thousands and hundreds place digits are both 2.

Step 2: Find the sum of the ones and tens digits
The problem states that the sum of the ones and tens digits is 14.

Step 3: Determine the possible numbers
We need to find the numbers that satisfy both conditions mentioned above.

Since the thousands and hundreds place digits are 2, the remaining digits are the ones and tens digits.

Let's consider the possible values for the ones digit (unit's place). Since the sum of the ones and tens digits is 14, the ones digit can be any number between 0 and 9 (inclusive) that, when added to the tens digit (which also ranges from 0 to 9), sums up to 14.

By trying different combinations, we can find the possible pairs of ones and tens digits that sum up to 14:
1 + 13 = 14
2 + 12 = 14
3 + 11 = 14
4 + 10 = 14
5 + 9 = 14
6 + 8 = 14
7 + 7 = 14
8 + 6 = 14
9 + 5 = 14
10 + 4 = 14
11 + 3 = 14
12 + 2 = 14
13 + 1 = 14

Now, we can combine the thousands, hundreds, tens, and ones digits using the possible pairs we found above to obtain the numbers:

2211
2220
1132
1141
1250
1340
1430
1520
1610
1700
1012
1021
1303

Therefore, the possible 4-digit numbers that satisfy the given conditions are:
2211
2220
1132
1141
1250
1340
1430
1520
1610
1700
1012
1021
1303.

You can double-check the calculations to ensure accuracy.