<p>i recently gave the maths level 2 but couldnt answer this question
s and r are positive integers
find s if s+10r=7^6 if s<10</p>
<p>Question’s basically saying, what’s the remainder when 7^6 is divided by 10 (hence the constraint 1 <= s <= 9). If you have a calculator, you can just evaluate 7^6 = 117649, so s = 9. If you don’t have a calculator, it is still fairly easy to find the remainder when 7^6 is divided by 10.</p>
<p>A bit of a different angle:
10r+s is number rs (s is written after all the digits of r), where s is units digit.
10x4 + 3 = 43,
10x25 + 7= 257,
10x123 + 4 = 1234, etc.</p>
<p>Since 10r+s = 7^6, s is the last digit of 7^6.
Without a calculator:
7^6 = 7x7x7x7x7x7.
7X7 = 49; 9 is the last digit of 7^2.
9x7 = 63, so 3 is the last digit of 7^3
3x7 = 21; 1 is the last digit of 7^4.
1x7 = 7; 1 is the last digit of 7^5.
7X7 = 49; 9 is the last digit of 7^6.</p>
<p>Because the last digits of 7^n repeat in a cycle of four (7, 9, 3, 1), this method would also work for high exponents.
For example, the last digit of 7^82 is 9 since
82 = 4x20 + 2, so 7^2 and 7^82 should have the same last digit.</p>
<p>yeah, it’s just about the units digit. do 7^6 on a calculator to see units digit is 9. So S decides that since 10R will always give units digit of 0. answer is 9</p>