QuestionAugust 26, 2025

Your Challenge Read the clues carefully to figure out the mystery number. The clues may describe more than one number. 1. It is a 4-digit number. The value of the digit in the thousands place is 10 times greater than the value of the digit in the hundreds place. The least digit is in the tens place. The sum of the digits is 19. The digit in the ones place is 4 more than the digit in the hundreds place. The mystery number could be __ The mystery number could also be __

Your Challenge Read the clues carefully to figure out the mystery number. The clues may describe more than one number. 1. It is a 4-digit number. The value of the digit in the thousands place is 10 times greater than the value of the digit in the hundreds place. The least digit is in the tens place. The sum of the digits is 19. The digit in the ones place is 4 more than the digit in the hundreds place. The mystery number could be __ The mystery number could also be __
Your Challenge Read the clues carefully to figure out the mystery number. The clues may describe more than one number. 1. It is a 4-digit number. The value of the digit in the thousands place is 10 times greater than the value of the digit in the hundreds place. The least digit is in the tens place. The sum of the digits is 19. The digit in the ones place is 4 more than the digit in the hundreds place. The mystery number could be __ The mystery number could also be __

Solution
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Answer

The mystery number could be 10135. Explanation 1. Define Variables Let the digits be a, b, c, and d for thousands, hundreds, tens, and ones places respectively. 2. Apply Clue 1 a = 10b 3. Apply Clue 2 c is the least digit. 4. Apply Clue 3 a + b + c + d = 19 5. Apply Clue 4 d = b + 4 6. Solve Equations Substitute a = 10b and d = b + 4 into a + b + c + d = 19: 10b + b + c + (b + 4) = 19 \Rightarrow 12b + c + 4 = 19 \Rightarrow 12b + c = 15 7. Determine Possible Values Since c is the smallest digit, try c = 0, 1, 2, 3, 4: - For c = 3: 12b = 12 \Rightarrow b = 1, a = 10, d = 5. Number: 10135 - For c = 4: 12b = 11 \Rightarrow b = 0.9167 (not possible) - For c = 2: 12b = 13 \Rightarrow b = 1.0833 (not possible) - For c = 1: 12b = 14 \Rightarrow b = 1.1667 (not possible) - For c = 0: 12b = 15 \Rightarrow b = 1.25 (not possible) 8. Verify Solutions Only valid solution is when c = 3, b = 1, a = 10, d = 5.

Explanation

1. Define Variables<br /> Let the digits be $a$, $b$, $c$, and $d$ for thousands, hundreds, tens, and ones places respectively.<br />2. Apply Clue 1<br /> $a = 10b$<br />3. Apply Clue 2<br /> $c$ is the least digit.<br />4. Apply Clue 3<br /> $a + b + c + d = 19$<br />5. Apply Clue 4<br /> $d = b + 4$<br />6. Solve Equations<br /> Substitute $a = 10b$ and $d = b + 4$ into $a + b + c + d = 19$: <br /> $10b + b + c + (b + 4) = 19 \Rightarrow 12b + c + 4 = 19 \Rightarrow 12b + c = 15$<br />7. Determine Possible Values<br /> Since $c$ is the smallest digit, try $c = 0, 1, 2, 3, 4$:<br />- For $c = 3$: $12b = 12 \Rightarrow b = 1$, $a = 10$, $d = 5$. Number: 10135<br />- For $c = 4$: $12b = 11 \Rightarrow b = 0.9167$ (not possible)<br />- For $c = 2$: $12b = 13 \Rightarrow b = 1.0833$ (not possible)<br />- For $c = 1$: $12b = 14 \Rightarrow b = 1.1667$ (not possible)<br />- For $c = 0$: $12b = 15 \Rightarrow b = 1.25$ (not possible)<br /><br />8. Verify Solutions<br /> Only valid solution is when $c = 3$, $b = 1$, $a = 10$, $d = 5$.
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