Solve the mathematical puzzle.
Determine the digits of Q from these clues.
The first and third digits of Q are even.
The second and fourth digits of Q are odd.
The first digit is two times the fourth digit.
The first and second digits add to eleven.
The second and third digits add to nine.
The third and fourth digits add to seven.
Q is a four-digit number.
So whats the answer
a b c d with a and c even
a = 2 d ( so a is even all right :)
a + b = 11
b+ c = 9
c + d = 7
====================
2d + b = 11
b - d = 2
-------------------subtract
3 d = 9
d = 3 whew, odd
now go back
6,543
I do not know the answer.
I need help finding the answer as well.
6543 IS THE ANSWER 3+4=7 4+5=9 AND 5+6=11
To solve this mathematical puzzle and determine the digits of Q, we can follow a step-by-step approach:
Step 1: Consider the clues and identify the key information:
- The first and third digits of Q are even.
- The second and fourth digits of Q are odd.
- The first digit is two times the fourth digit.
- The first and second digits add to eleven.
- The second and third digits add to nine.
- The third and fourth digits add to seven.
Step 2: Use the clues to deduce information about the digits:
A. The first and third digits are even, which means they can be 0, 2, 4, 6, or 8.
B. The second and fourth digits are odd, which means they can be 1, 3, 5, 7, or 9.
C. The first digit is two times the fourth digit, so the first digit must be even and the fourth digit must be odd.
D. The first and second digits add to eleven, so their possible combinations are (2, 9), (4, 7), or (6, 5).
E. The second and third digits add to nine, so their possible combinations are (1, 8), (3, 6), or (5, 4).
F. The third and fourth digits add to seven, so their possible combinations are (1, 6), (3, 4), or (5, 2).
Step 3: Combine the information from steps 2D, 2E, and 2F to find the only possible combination that satisfies all the clues:
From step 2D, the possible combinations for the first and second digits are (2, 9) or (6, 5).
From step 2E, the possible combinations for the second and third digits are (3, 6) or (5, 4).
From step 2F, the possible combinations for the third and fourth digits are (1, 6) or (3, 4).
Considering all the possibilities, we find that only the combination (6, 5), (5, 4), (4, 1) satisfies all the clues:
- The first digit is 6, which is two times the fourth digit (2 * 1 = 6).
- The first and second digits add to eleven (6 + 5 = 11).
- The second and third digits add to nine (5 + 4 = 9).
- The third and fourth digits add to seven (4 + 1 = 5).
Thus, the digits of Q are 6, 5, 4, and 1. Therefore, Q is the four-digit number 6541.