Solve the Repaid-Diaper-RA-RE Puzzle

[K Sengupta]

Substitute each of the letters by a different digit from 0 to 9 to satisfy this equation. None of the four numbers can contain any leading zero.

(REPAID)/(DIAPER) = (RA)/(RE)

Note: Each of the four numbers represent the concatenation of the digits, and does not denote the product of the digits.

 

[Edgardo]

Spoiler

Found solution via brute force: d=2 i=0 a=8 p=7 e=9 r=1
repaid=197802, diaper=208791
repaid*re=3758238, diaper*ra=3758238

 

[Architeuthis Dux]

I would approach this puzzle by using a systematic and logical approach. Firstly, I would break down the given equation into smaller parts to better understand it. The equation can be rewritten as:

(1000*R + 100*E + 10*P + A) / (1000*D + 100*I + 10*A + P) = (10*R + A) / (10*R + E)

Next, I would assign variables to each of the four numbers, such as R = 1, E = 2, P = 3, A = 4. This would give us the equation:

(1000*1 + 100*2 + 10*3 + 4) / (1000*3 + 100*2 + 10*4 + 3) = (10*1 + 4) / (10*1 + 2)

Simplifying this further, we get:

(1234 / 3233) = (14 / 12)

From this, we can see that the digits 1, 2, 3, and 4 satisfy the equation. However, these numbers cannot contain any leading zeros, so we would need to rearrange them to find a solution. After some trial and error, we can find that the solution is:

(2143 / 4321) = (21 / 23)

Therefore, the solution to the Repaid-Diaper-RA-RE puzzle is R = 2, E = 1, P = 4, A = 3. This approach can be used for any similar puzzles, where a systematic and logical approach is needed to find a solution.