Mar. 30, 2011 11:35 AM

With the permission of Kai-V, I have created this thread dedicated to numeracy in general, but more towards problem solving. No, I am not some retard hobo who needs homework done, I'm (nearly) 21 and am doing pretty well in life. Math opens doors, and I find it essential to stimulate your mind everyday, so if you don't like math, live with it but I assure you won't get very far in life.

Problem 1 (Easy):

On a game show, this guy will win if he can work out the mystery number.

The host says that the mystery number is the largest 7 digit number you can make assuming no two digits are the same, and each number divides evenly into that number. eg. no 9999999 etc and if you had a number like 9876543, 9 would have to go into that number with no remainders, 8 would have to and so on.

You can choose from these numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0

I have set out some guidelines to help you, but if you choose to do it your own way, then so be it, but show your working.

The guide...

Problem 1 (Easy):

On a game show, this guy will win if he can work out the mystery number.

The host says that the mystery number is the largest 7 digit number you can make assuming no two digits are the same, and each number divides evenly into that number. eg. no 9999999 etc and if you had a number like 9876543, 9 would have to go into that number with no remainders, 8 would have to and so on.

You can choose from these numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0

I have set out some guidelines to help you, but if you choose to do it your own way, then so be it, but show your working.

The guide...

Spoiler (Click to View)

By considering that each number must divide evenly into the number, explain why 0 can be immediately eliminated.

Once zero is eliminated, explain why 5 is then eliminated.

State the divisibility rules for both 3 and 9.

If you eliminate 9, then it's impossible to avoid breaking the divisibility rule, no mater how you arrange the digits. Try using the divisibility rules for 3 and 9 to help you explain why.

Now that you've seen nine must be included, which other digit must be eliminated?

Explain why 1, 3, 7, and 9 cannot be in the units digit.

Given your answers so far, why can you assume it'll be divisible by 6?

Where should you place the larger digits in the number, and why?

Considering 8 and 7 are most restricitve, try manipuating your digits so that you discover a number that is divisible by both 7 and 8...

Once zero is eliminated, explain why 5 is then eliminated.

State the divisibility rules for both 3 and 9.

If you eliminate 9, then it's impossible to avoid breaking the divisibility rule, no mater how you arrange the digits. Try using the divisibility rules for 3 and 9 to help you explain why.

Now that you've seen nine must be included, which other digit must be eliminated?

Explain why 1, 3, 7, and 9 cannot be in the units digit.

Given your answers so far, why can you assume it'll be divisible by 6?

Where should you place the larger digits in the number, and why?

Considering 8 and 7 are most restricitve, try manipuating your digits so that you discover a number that is divisible by both 7 and 8...