Using Arduino to create a countdown that unlock a box

This sounds as an escape room puzzle. From an electronic point of view you need something to lock/unlock the box like a servo motor, a stepper motor or (best option) a normally closed solenoid. You might need some components to drive such locking mechanism, like a mosfet or transistor (possibly a darlington), depending on which device you choose and what voltage it requires to operate. Simplest solution is a servo motor which doesn’t require anything, but has a low torque, meaning the box can easily be forced. Most robust and reliable solution is a NC solenoid, common ones are 12V so you’ll need a p-channel enhance mosfet and a couple of resistors to drive it from an Arduino.

To display the time you’ll probably want to go for an LCD, common ones are 16 col x 2 rows, most have an integrated chip to drive them using only a few wires.

Apart from that, you need a battery pack (voltage and power depending on your locking circuit choice) and may be a push button (for safety unlock).

From a software perspective you want to create a loop which starts by locking the box and then counts down the time: when the time left is less than 5 mins it activates the unlocking mechanism circuit.

int current = 0;
const int max = 2 * 60 * 60; // 2hrs in sec
const int grant = 5 * 60; // 5mins in sec
bool unlocked = false;

void setup() {
    lock();
}

// executed once every second
void loop() {
    // any safety open check should be performed here...
    // if still locked and less than 5 mins to end
    if (!unlocked && current > max - grant) {
        unlock();
    }
    
    display(current++);
    wait(1000);
}

// does what it is needed to unlock and sets the unlocked variable to true
void unlock() { ... }

// does what it is needed to lock and sets the unlocked variable to false
void lock() { ... }

void display(int secs) {
    int h = secs / (60 * 60);
    int m = (secs / 60) % 60;
    int s = secs % 60;
    // display on LCD the values above with the proper formatting
}
    

A couple of notes:

• if you go for a normally closed solenoid be sure to have a way to get inside the box if something goes wrong with your circuit or if the batteries get drained
• you might want to have a hidden button or other way to force the unlock, especially for debugging and testing