There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?

"Let's assume the 3rd digit is 'x'. Then, the 2nd digit would be '4x', and the 1st digit would be '4x-3'. Based on this scenario, there are two possible solutions: If the digits are allowed to repeat, the answer is 141. If the digits are not allowed to repeat, the answer is 582."

582. can be done by guesswork

Let the third digit be $$x$$ Therefore, the second digit is 4x The first digit is 4x-3 The original number is 4x-3+ 10(4x) + 100x = 144x-3 Substitute x=0, it follows: The number will be 0-3=-3 (rejected) Substitute x=1, it follows: The number will be 144-3=141 Substitute x=2, it follows: The number will be 288-3=285 Substitute x=3, it follows: The number will be 432-3=429 Substitute x=4, it follows: The number will be 576-3=573 Substitute x=5, it follows: The number will be 720-3=717 Substitute x=6, it follows: The number will be 864-3=861 Substitute x=7, it follows: The number will be 1008-3=1005 (rejected) The possible numbers are 141, 285, 429, 573, 717, 861

Let's denote the three-digit number as ABC , where A is the first digit, B is the second digit, and C is the third digit. According to the problem: 1. The second digit B is four times the third digit C B = 4C 2. The first digit A is three less than the second digit B A = B - 3 Now, let's find the digits: - Since B = 4C , B must be a digit between 0 and 9, and C must be an integer such that 4C is still a digit (i.e., between 0 and 9). The only value C can take is 1 because 4 times 1 = 4 . Therefore: C = 1 , B = 4 x 1 = 4 - Now, substitute B = 4 into the equation for A : A = 4 - 3 = 1 So, the digits A, B, and C are 1, 4, and 1, respectively. Therefore, the three-digit number is **141**.

141