4KM and 4KJ had a maths problem to solve – I couldn’t resist sharing my solution.

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Today’s Problem: Sealed Solution

Hello 4KM and 4KJ,

I think you already know I love a maths challenge. Seeing your post for your special visitors, I saw the included challenge and thought I would share my solutions. For others, here was the challenge for the students and special visitors.

This problem is from the NRICH website.

There are 10 cards each bearing the digits 0 to 9. Two are placed in each of five envelopes. The sum of the two cards in each envelope must match the number on the envelope. The challenge was to find what two cards could be in the envelope numbered 8. The students and visitors were informed there was more than one solution. See the below graphic...

Number envelopes

 

How did I find my solutions?

1. The challenge stated the two cards in each envelope are added to reach the number on the envelope (the sum of the two cards).

2. Being ten cards each bearing a digit from 0 to 9, I assumed each digit could only be used once.

3. Next I looked at the target, Envelope 8. Using the cards, what 2 card combinations could give the sum of 8? Here they are..

8 + 0 = 8

7 + 1 = 8

6 + 2 = 8

5 + 3 = 8

4. Now I drew up a grid to test each of the sums to see if all four could be correct. I found three worked but one failed. Here are the three successful answers...

3 + 4 = 7    8 + 0 = 8   6 + 7 = 13   9 + 5 = 14   1 + 2 = 3

2 + 5 = 7    7 + 1 = 8   9 + 4 = 13   8 + 6 = 14   3 + 0 = 3

7 + 0 = 7    5 + 3 = 8   9 + 4 = 13   8 + 6 = 14   1 + 2 = 3

Therefore, Envelope 8 could only contain 0 and 8, 1 and 7, or 3 and 5.

 

Why did 2 and 6 fail?

Envelope 14 can only contain 8 and 6 or 9 and 5 to give the sum of 14. As  2 and 6 (6 + 2 = 8) have been used, 8 and 6 aren't possible but what about 9 + 5 =14?

Envelope 13 can only contain 9 and 4, 8 and 5 or 7 and 6 if the sum is to be 13. If we have already used 2 and 6 (2 + 6 = 8) and 5 and 9 (5 + 9 = 14), we can't use any solution for Envelope 13. Therefore 6 + 2 = 8  is not a solution.

How did I do?

4 thoughts on “4KM and 4KJ had a maths problem to solve – I couldn’t resist sharing my solution.

  1. Hialle

    Hi Ross, 😆

    My name is Haille and I am in 4KM.
    I enjoyed reading your post and solutions, you must really enjoy doing maths (I do).

    This has nothing to do with this, but if you want to visit my blog,click on the link below.
    Haille’s Blog

    From,
    Haille :mrgreen:

    Reply
    1. rossmannell

      Post author

      Hello Haille,

      I have enjoyed maths since primary school. My interest in maths and science have worked well together but, as people can see in this blog, I’m interested in very many things.

      When I saw the maths challenge on your class blog, I was curious so I set about finding the solution. I found three possible answers.

      The link to your blog didn’t work but I was able to track down the correct link on your class blog so I’ll visit within the next day or two. The link to your blog is…
      http://haille.global2.vic.edu.au/

      Ross Mannell

      Reply
      1. Haille

        Hi Ross,

        Sorry that the link didn’t work.

        Today was pop maths day and the maths things that we did were really fun. I was in group sharks.

        Do you know what pop maths day is?

        From,
        Haille. :mrgreen:

        Reply
        1. rossmannell

          Post author

          Hello Haille,

          No problem with the link error. I’ve also made that type of mistake. 🙂

          Pop quizzes have been around for some time. I think I first heard of them in American classes where the teacher surprised the class with a quiz. Pop maths day sounds like it’s a surprise day of maths fun activities. I think I’d enjoy that. 🙂

          Ross Mannell

          Reply

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