Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Which is 6? I don't know.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Let's forget the answer for now. We just agreed that taking any number mod 10 gets the last digit.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

K I agree, you agree, we agree.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

So if we could mod 10 that whole expression we would get the unit digit of it and solve the problem.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

I see

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Now the mod operator as I told you can be split up:

is the same as

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

I see

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

If you take the mod 10 of each parentheses you will get a 6 for each parentheses.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

I see but then we will have to multiply them?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Yes but you will take the mod 10 of each pair.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

I see, sorry was eating.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

( 6 x 6 ) mod 10 = 6

( 6 x 6 ) mod 10 = 6

( 6 x 6 ) mod 10 = 6

( 6 x 6 ) mod 10 = 6

Now you only have 4 sixes.

( 6 x 6 ) mod 10 = 6

( 6 x 6 ) mod 10 = 6

Now you only have 2.

( 6 x 6 ) mod 10 = 6 and you are done. Notice the first way was easier. See you a little later.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Thanks for your time and everything bobbym. See you later too.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Do you understand everything up to here?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Yes

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Okay, then we will cover a few more when I get them ready.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi chooipian;

This one is easy so we will start there.

What is the units digit of

or

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Explain

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

It is a 1.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

How does it work again?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

8^2014 is really 8 x 8 x 8 x 8 when there are 2014 8's. Yes?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Yes.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Take a look at post #56 again as a review.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

I just did.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

So what do you say about

(8 x 8 x 8 x 8 ... 8) mod 7 ?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline