On the eve of the new year I want to offer you an interesting and simple exercise. I hope this year was good and fruitful for you!
What is the unit's digit of 20172017+20182018 ?
The solution of the problem will be slightly lower.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Solution:
The units digit of 20172017 is same as 72017 and the units digit of 20182018 is same as 82018.
It is easy to see that 71 ends with 7, 72 with 9, 73 with 3, 74 with 1 and 75 again with 7. So period is 4 and 72017=71+2016, hence, it ends with digit 7.
Similarly, we get for 82018 = 82+2016 and it ends with 4.
So 4+7=11 and the sum ends with digit 1.
