The Last Digit Riddle

A monk says: “I’ve written down a very large number — it’s 2 raised to the 57th power.
Without a calculator or looking it up, can you tell me what the last digit is?”

Answer:

👉 2


Explanation:

This riddle is all about recognizing patterns in powers of 2.
Let’s look at the last digits of the first few powers of 2:

  • 2¹ = 2
  • 2² = 4
  • 2³ = 8
  • 2⁴ = 16 → last digit is 6
  • Then it repeats: 2, 4, 8, 6…

So, the last digits repeat every 4 powers:
[2, 4, 8, 6]

Now, divide 57 by 4:

  • 57 ÷ 4 = 14 remainder 1

That means 2⁵⁷ has the same last digit as , which is:
👉 2

17
15