"Brilliant" Logic

Logic Level 2

I am thinking of $n$ , a positive integer, and I use it as follows to obtain a value for $k$

$k = \frac{\bigg(n^n \mod{10}\bigg)}{2},$

What is my value of $k$ ?

Hint: You have 3 tries to get this problem correct and using "Brilliant" logic you can work it out.

The answer is 3.

2 solutions

Stephen Mellor
Apr 17, 2018

As we are considering $n^n$ Mod 10 , we only need to calculate the result for single digit $n$ since, for example $2^2 = 12^{12}$ when both Modulo 10.

n	n^n Mod 10	(n^n Mod 10) / 2
1	1	0.5
2	4	2
3	7	3.5
4	6	3
5	5	2.5
6	6	3
7	3	1.5
8	6	3
9	9	4.5
10	0	0

(note that 10 has been used rather than 0 for numbers $n$ which end in 0 since 0 is not a positive integer and could cause problems if it was included)

Now Brilliant would display a message above the answer box saying "Decimals OK" if the answer was a decimal. Since this can't be seen, the answer is an integer so is one of 0,2 or 3, which you can guess all of them as three guesses are allowed

Steven Jim
Apr 6, 2018

Okay. Let's say this problem has its problems, but indeed it's good Logic (that I have to admit) so stop blaming each other.

Note here that if (s)he means 'decimal OK' then (according to him/her) $n$ must be even, as when $n$ is odd, $k$ is an integer.

Also, $n^n$ mod 10 can only be $0,4$ or $6$ , or $k=0.5,2.5$ or $k=3.5$ . And as you have 3 tries, use all 3 and you will definitely have a correct answer.

As Siva Budaraju pointed out, 'Decimals OK' does not mean the answer must not be an integer. I have like 6 or 7 problems that I use this technique in just in case they guess the answer.

@Calvin Lin You might want some serious fixing on this problem, even though it is good.

Now you come to mention it, I have seen problems where I have inputted 7 as my answer and Brilliant has said "Correct, the answer is 7.000"

Stephen Mellor - 3 years, 2 months ago

Yeah... You need to make things easy to understand there :D

Steven Jim - 3 years, 2 months ago

@Steven Jim The problem has been changed so your solution could just be tweaked a bit to make it consistent. I hope this removes ambiguity

Stephen Mellor - 3 years, 2 months ago

Maybe I would've been better if I hadn't added one, and then the 3 options would've been integers. That way, the inverse logic definitely works, since you can't convert a decimal into an integer

Stephen Mellor - 3 years, 2 months ago

That’s good then :)

Steven Jim - 3 years, 2 months ago

Why can't n be odd? Where does it say in the problem that k is an integer?

Tom Shillington - 3 years, 2 months ago

This is a solution from before the problem was changed. You now know that the final answer must be an integer because Brilliant doesn't say "DecimalsOK" above the answer box

Stephen Mellor - 3 years, 2 months ago

"Brilliant" Logic

The answer is 3.

2 solutions

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