# Star equation

Write digits instead of stars so that the sum of the written digits is odd and is true equality:

42 · ∗8 = 2 ∗∗∗

Result

b1 =  48
b2 =  68
c1 =  2016
c2 =  2856

#### Solution:

$a=42 \ \\ s_{1}=a \cdot \ 18=42 \cdot \ 18=756 \ \\ s_{2}=a \cdot \ 28=42 \cdot \ 28=1176 \ \\ s_{3}=a \cdot \ 38=42 \cdot \ 38=1596 \ \\ s_{4}=a \cdot \ 48=42 \cdot \ 48=2016 \ \\ s_{5}=a \cdot \ 58=42 \cdot \ 58=2436 \ \\ s_{6}=a \cdot \ 68=42 \cdot \ 68=2856 \ \\ s_{7}=a \cdot \ 78=42 \cdot \ 78=3276 \ \\ 2000 <=s <=2999 \ \\ S=\{ 2016, 2436, 2856 \} \ \\ x_{1}=4+0+1+6=11 \ \\ x_{2}=5+4+3+6=18 \ \\ x_{3}=6+8+5+6=25 \ \\ x_{1}=nepar \ \\ b_{1}=48$
$b_{2}=68$
$c_{1}=a \cdot \ b_{1}=42 \cdot \ 48=2016$
$c_{2}=a \cdot \ b_{2}=42 \cdot \ 68=2856$

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