Question 1
We call a positive integer *sunny* if it has four digits and if moreover each of the two digits on the outside is exactly 1 larger than the digit next to it. The numbers $8723$ and $1001$ for example are sunny, but $1234$ and $87245$ are not.
a) How many sunny numbers are there such that twice the number is again a sunny number?
b) Prove that every sunny number greater than $2000$ is divisible by a three-digit number with a $9$ in the middle.
a) How many sunny numbers are there such that twice the number is again a sunny number?
b) Prove that every sunny number greater than $2000$ is divisible by a three-digit number with a $9$ in the middle.