Problem 9 · Three clues, three digits
Everything in terms of the tens digit: $4d = 16$.
Integer answer, at most 4 digitsWhich three-digit number satisfies the following properties?
- The sum of its digits is $15$.
- The hundreds digit is twice the tens digit.
- The tens digit equals the units digit plus $1$.
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: express hundreds and units in terms of the tens digit $d$: $c = 2d$ and $u = d - 1$.
$$c + d + u = 2d + d + (d-1) = 4d - 1 = 15 \;\Longrightarrow\; d = 4.$$
Then $c = 8$ and $u = 3$: the number is $843$. (Check: $8 + 4 + 3 = 15$ ✓.)
Answer: 843