Every morning, on the school run, my kids and I tune in to Radio Bahrain’s Martin and Hayley in the Morning. Lately, they have been running a new game: Callers try their luck at cracking a safe by guessing a four-digit code to win what’s inside.
As a mathematician and data scientist, I can’t resist turning moments like this into a numbers game.
“Kids, do you know how many people would have to call before someone finally cracks the safe if nobody gets it right early and no one repeats a guess?”
Their eyes widened when I told them: 10,000 calls. That’s every possible four-digit combination. Assuming five contestants calling each day, five days a week, it would take about seven-and-a-half years before the safe is guaranteed to open unless someone gets lucky.
“Is that really possible, or is it just me being a pessimistic mathematician?” I asked myself.
Surprisingly, the long wait could happen. And it’s more likely than we think for two reasons:
First, psychology. People rarely pick numbers at random. Instead, they lean toward ones that feel familiar, personal or lucky. Something like their phone numbers, car plates, bank PINs or birthdays. We trust the numbers tied to our lives far more than any random number.
Second, statistics. Even when people believe they’re guessing at random, human choices aren’t evenly spread. In practice, callers are far more likely to guess numbers that feel comfortable or manageable like the small numbers in the 1000s or 2000s than to leap toward something big like 8739 or 9625. The result: The higher number those in the 8000s and 9000s remain neglected for much longer, dragging out the game far beyond what pure chance would suggest.
Can we turn all this into a winning strategy for cracking the safe? Maybe, but I’m still skeptical. Unless the hosts drop a real hint, the odds remain against us. If the code was chosen by a human, the best guess might be to look for a number tied to the show itself or aim for the more popular ranges, like the 1000s or 2000s, might slightly improve the chances.
The author is a PhD in Mathematics
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