Imagine Your Broken Calculator Maxes Out at a Trillion. Can You Still Solve this Puzzle?
Saturday 24 October 2026 at 13:22
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Edited by Richard Walker, Saturday 24 October 2026 at 14:20
Imagine your calculator is broken. It won't handle numbers beyond 1,000,000,000,000 but you have been asked to find the last two digits of .
Can you still find the answer. What is it?
Scroll down for Solution and Discussion.
Solution
Even with the broken calculator we can start calculating some small powers of and when we get to we discover the last two digits are . This means all end in (01\).
So will end in also and to find the last two digits of we can just multiply by , which tells us the answer is .
In fact it is possible to prove the rather astonishing fact, that for any prime , has the same last two digits as .
And so for example we can be sure that the last two digits of , a number of some 2,000 digits, are .
Imagine Your Broken Calculator Maxes Out at a Trillion. Can You Still Solve this Puzzle?
Imagine your calculator is broken. It won't handle numbers beyond 1,000,000,000,000 but you have been asked to find the last two digits of .
Can you still find the answer. What is it?
Scroll down for Solution and Discussion.
Solution
Even with the broken calculator we can start calculating some small powers of and when we get to we discover the last two digits are . This means all end in (01\).
So will end in also and to find the last two digits of we can just multiply by , which tells us the answer is .
In fact it is possible to prove the rather astonishing fact, that for any prime , has the same last two digits as .
And so for example we can be sure that the last two digits of , a number of some 2,000 digits, are .