Break your calculator with this
What is the last digit of 1 5 4 4 6 4 5 3 5 3 4 5 3 4 5 3 4 7 5 8 2 6 7 1 2 4 5 5 6 7 5 6 7 5 8 4 3 4 5 3 5 3 4 5 3 4 5 ?
The answer is 7.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
3 solutions
It's probably better to say that the exponent is equal to 1 in modulo 4, or is 1+4n, where n is an integer.
Great job with your solution, by the way.
I did some tests. Every number^5 will preserve the last digit from the initial value.
Nice solution!
The last digit of 1 5 4 4 6 4 5 3 5 3 4 5 3 4 5 3 4 7 5 8 2 6 7 1 2 4 5 5 6 7 5 6 7 5 8 4 3 4 5 3 5 3 4 5 3 4 5 is 7 5 = 7 × 7 × 7 × 7 × 7 = 4 9 × 7 × 7 × 7 = 3 4 3 × 7 × 7 = 2 4 0 1 × 7 = 1 6 8 0 7 = 7 . So, the answer is 7 .
Since we are only concerned with the last digit, we can work in modulo 10. In modulo 10: 7^1=7, 7^2=9, 7^3=3, 7^4=1, 7^5=7 then the list repeats.
In general, for whole number n, 7^(1+4n)=7, 7^(2+4n)=9, 7^(3+4n)=3,
Since the exponent in divisible by 5, it can be expressed as 1+4n for some n.
Therefore, the last digit is 7.