The Lockers
Delphine and Théo
each have a locker.
Lockers
are numbered from 1 to 99.
The
two digits of Delphine’s locker number are the same as those
in Théo’s, but in reverse order.
If you
add the two digits of Delphine’s locker number, the sum is
exactly equal to the difference between Delphine’s and
Théo’s locker numbers.
Question: What are
their locker numbers?
Answer:
Let’s say
Delphine’s locker number is AB, where:
- A is
the tens digit
- B is
the units digit
So her
number = 10A + B
Théo’s
locker is BA = 10B + A
Given:
- A +
B = (10A + B) – (10B + A)
Let’s
find values of A and B between 1 and 9 that satisfy this:
Try A
= 2, B = 1
Delphine
= 21, Théo = 12 → Difference = 9
Sum of
digits = 2 + 1 = 3 ❌
Try A
= 4, B = 5
Delphine
= 45, Théo = 54 → Difference = 9
Sum =
4 + 5 = 9
Final
Answer
- Delphine’s
locker: 45
- Théo’s
locker: 54
