Question 6
Answer all ten questions and show detailed solutions. Printed time 60 minutes; each question 4 points. Subcriterion allocations are editorial.
The number 132 has three distinct digits and equals the sum of all different two-digit numbers made from those digits: $132=13+12+21+23+31+32$. Find all other three-digit numbers with this property.
The number 132 has three distinct digits and equals the sum of all different two-digit numbers made from those digits: $132=13+12+21+23+31+32$. Find all other three-digit numbers with this property.