Maths Problem

A new Maths problem!

 
Housey housey points on offer to the fastest!!
 
How much can we spend?
A country has decided to have just two different coins.

It has been suggested that these should be 3z and 5z coins.

The shops think this is a good idea since most totals can be made:
 


Unfortunately some totals can't be made, for example 4z.
Which totals can be made?
Is there a largest total that cannot be made?
How do you know?
They have decided that they will definitely have 3z coins but can't make up their minds about the other coin.
 
Experiment with other pairings containing 3z.
Which totals can be made?
Can you find a rule to help you predict which totals can be made?
What is the largest total that cannot be made?
How do you know?
In other countries they have also decided to have just two coins, but instead of the 3z coins they have chosen a different prime number.

Can you find rules to help you predict what totals are possible for different pairings?

19 comments:

  1. Lucy13 March 2014 at 14:54

    The totals that can be made is: 8z, 6z, 7z, 9z, 13z, 4z, 5z, etc..
    The rule is : when 3 add another number it becomes the next number. Like for example 3+1= 4, 3+2=5, 3+3=6, and etc....

    ReplyDelete
  2. Anonymous13 March 2014 at 18:43

    Part 1
    When using a 3z and a 5z you can make totals that end with 0,3,5,6,8 and 9. You can't make totals that end with 1,2,4 and 7. There is no largest total. Numbers are infinite.
    Part 2
    The other coin should be 1z. It should be 1z because you could make any number.

    Long

    ReplyDelete
  3. Anonymous13 March 2014 at 20:45

    Part 1
    The totals that can be made with a 3z and a 5z are totals that end with 0, 3, 5, 6, 8, and finally 9. There is no largest total that can't be made because numbers are infinite.

    Part 2
    1z, because any number can be made with 1z.

    ReplyDelete
  4. Anonymous14 March 2014 at 20:13

    The totals that can be made are 0, 3, 5, 6, 8 and 9 if using 3z and 5z. There is no biggest total because all numbers just go on and on. The new coin should be 1z because you can make as many numbers as you want with just 1z. (But if you want to pay for something pricey with lots of 1z, there would be lots of counting to do...)

    ReplyDelete
  5. Anonymous15 March 2014 at 10:53

    1st:
    The totals that can be made for 3z and 5z are: 3z, 5z, 6z, 8z, 9z, 10, 11z, 12z, 13z...etc
    The totals that cannot be made are: 7z, 14z 22z
    The numbers 7z, 14z, 22z can't divide by 3z and 5z(added together equals 8) evenly, therefore they cannot be made.

    2nd:
    I think that the other pair should be 1z and 3z because, with 1z, you can make ANY number. Like; 3z, 4z, 5z ,6z...∞ BUT, you cannot make decimals because we don't have 0.5z coin.

    3rd:
    I think that the other countries can use 1z and 5z coins because this pair can also make any numbers including ∞
    The rules to help me predict what totals are possible for different pairings are that the totals need to be even numbers and composite numbers.


    Abby :3
    P.S: It took me 1 hour to work it out...

    ReplyDelete
  6. Anonymous15 March 2014 at 19:07

    Part 1:
    Totals that can be made from 3z and 5z are: 3z , 5z, 6z, 8z, 9z, 10z, 11z, 12z, 13z, 14z, 15z, 16z,... Totals that can't be made from 3z and 5z are only: 1z, 2z, 4z, 7z. The largest number that can't be made is 7. You can still pay 1z, 2z, 4z, and 7z. For example: A chocolate bar is 1z, you can still pay 6z (using two 3z coins) and get change for 5z. Pay 2z for two chocolate bars by paying 5z and get 3z back. If a drink is 4z you can pay 9z and get 5z as change and 7z for some chewing gum can be paid by giving 10z and getting 3z back.

    Part 2:
    The other pair should be 1z and 3z because any number can be made with 1z (only if the country doesn't use decimals). Totals that can be made are: 1z, 2z, 3z, 4z, 5z, 6z... All numbers can be made. Therefore, there isn't a largest total (except 0).

    Part 3:
    Other country SHOULD use 1z and 3z coins. Unfortunately, 1 isn't a prime number. So that means: 2z and 3z coins should be used.(Also because the question said:In other countries... have chosen a different PRIME NUMBER.)

    Jasmine :D

    ReplyDelete
    Replies
    1. Anonymous19 March 2014 at 16:36

      Also the reason why I chose 2z and 3z is most numbers can be made except for 1z.

      Delete
  7. Sebastian15 March 2014 at 21:54

    Part 1
    You can only use 3z and 5z so you can make: 0z, 3z, 5z, 6z, 8z, 9z, 10z and you can do this forever.

    Part 2
    The next number should be 1z because you can use 1 for everything like 1+1=2, 1+1+1=3 and you can do this forever again.

    ReplyDelete
  8. Francis17 March 2014 at 17:45

    Part 1
    You can make all sorts of totals that end in 0,1,2,3,5,6, 7,8 and 9z there is no largest number probably because the numbers can go on forever because you can times the 5z coins by as much as you want.
    Part 2
    I would pair the 3z coin with a 1z coin because it can make any other number but the bad thing is that it might be very inconvenient to be carrying so many coins with you.
    Part 3
    I would choose the 1z coin and the 5 z coin because this is a bit more convenient then the part 2 and also it can make an endless amount of possibilities too.

    ReplyDelete
  9. Anonymous17 March 2014 at 18:28

    the numbers 3,5,6,8,9 can be made and this sequence can go on forever

    you should probably use a 1z coin because it can make every single number and can go on forever.

    Nicholas 6T

    ReplyDelete
  10. Anonymous17 March 2014 at 20:35

    Examples of totals that can be made:
    3,5,6,36,51,65

    Examples of totals that can't be made:
    1,2,4,13, 22

    There are no largest total that can be made ; numbers are infinite (goes on forever) and there are many totals that can't be made that are really big.

    The other number should be 1zed because any total can be made with the number 1 - any number is divisible by 1 but if we use 1, it would be very inconvenient. So if I were to choose a completely different pair of zeds, I would pick 2zeds and 1zed every total can be made.

    Rose




    ReplyDelete
    Replies
    1. Rose18 March 2014 at 21:21

      I made a minor mistake in the last sentence. It should be:

      So, if I were to choose a completely different pair of zeds, I would pick 2zeds and 3zeds since most totals can be made.

      Rose :)

      Delete
  11. Anonymous19 March 2014 at 18:32

    Totals that can be made are all multiples of 3, 5 and 8, there can not be a largest total because numbers are infinite.
    I would pick 1 zed to be the last coin because any totals can be made using it.

    ReplyDelete
  12. Anonymous19 March 2014 at 19:48

    HELLO! IM NICHOLAS! 6T

    Random Math question that came to me from somewhere over the rainbows

    a store sale is 40% off then it increases how many % new price = original price!

    Comment on my post.

    Winner gets uh iuhsdiuhiuhuifiunf to fly over a rainbow with a leprechaun oh and the leprechaun pot is filled with bacon... Justin go ahead and answer the question first!

    TIP for Michael to win: DONT TYPE TIRTY TREE

    ReplyDelete
    Replies
    1. Anonymous25 March 2014 at 22:54

      The answer is 66.66666.......etc. Give me the leprachaun pot filled with bacon!

      Delete
    2. Anonymous25 March 2014 at 23:10

      Too slow Justin!

      Delete
  13. Anonymous25 March 2014 at 23:09

    Part 1
    We can make 3, 5, 6, 9, 10, 12, 15,........
    There is no largest total because numbers are infinite.

    Part 2
    I would have 1z with 3z because you can make anything with 1z.
    There is no largest total that cannot be made because 1z can make any numbers.

    Part 3
    A 2z coin should be with the 3z coin because you can make most of the numbers with these coins.

    ReplyDelete
  14. Anonymous31 March 2014 at 08:43

    Part 1
    We can make 3,5,6,8,9,10,12, etc.
    Numbers are infinite so there is no largest total.

    Part 2
    I would have 3z with the 1z because with 1 you can make any total
    Same reason as part 1 for why there is no largest total

    Part 3
    If 1 is not prime, then I would go for 5z and 2z because all totals can be made except 1z and 3z.

    ReplyDelete
  15. Anonymous14 April 2014 at 19:54

    Khanh 6T!
    We can make 3,5,6,8,9,10,12,13 etc.
    Numbers are infinite so there is no largest total.
    I'd have 3z and 1z because any number( except from decimals) can be made. There is no biggest total( same reason).

    ReplyDelete

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