The 5-digit number PQRST (all distinct digits) is such that $T \ne 0$. P is thrice T. S is greater than Q by…
The 5-digit number PQRST (all distinct digits) is such that $T \ne 0$. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?
3
4
5
6
Solution
Conditions: $P = 3T$ (with $T\ne0$), so $T\in\{1,2,3\}$ giving $P\in\{3,6,9\}$. Also $S = Q+4$ and $Q = R+3$, so $S = R+7$, with all digits 0-9 and distinct. Possible $R$: $S=R+7\le9$ gives $R\in\{0,1,2\}$, yielding $(R,Q,S) = (0,3,7),(1,4,8),(2,5,9)$. Combining with valid $(T,P)$ pairs and ensuring all five digits are distinct yields 4 valid numbers.