Problem $1$: $(10$ points$)$

Prompt the user for a number $n.$ Find the number of digits in the number. Do NOT

use string length.

Problem $2$: $(10$ points$)$

Create a guessing game. Pick any number between $1$ and $1000.$ Prompt the user

to guess numbers until the player guesses the correct number. For every guess,

output "Too high" or "Too low", and then ask for another input. At the end of the game,

the number is revealed along with the number of guesses it took to get the correct

number.

Problem $3$: $(10$ points$)$

Prompt the user for a number $n.$ Check if the number is an Armstrong number i$.$e$.$

sum of the cube of individual digits returns the same number. For example, $153$ is

an Armstrong number since $1^3+5^3+3^3=153\mathrm{.}371$ is another example.

Problem $4$: $(10$ points$)$

Prompt the user for a number $n.$ Check if the number is a binary number or not i$.$e$.$

all digits in the number must be either $0$ or $1.$ For example, $101$ is a binary number

whereas $123$ is not. Note: $0$ and $1$ are the only single digit binary numbers.

Problem $5$:$(10$ points$)$

Prompt the user for a number $n.$ Check if the number is composite i$.$e$.,$ the number

is NOT prime and hence it is divisible a number other than $1$ an

d itself. For

example, $1,3,5,7$ is prime whereas $4,6,8,9$ are composite.

JAVA