We had a very large number of solutions come in for this challenge. Here are a selection for you to consider.
Primary 6 at Victoria Primary School in Scotland sent in this very thorough solution
Firstly, we looked at the 4 numbers at the bottom and tried to work out how to get to 15. As a class we agreed that this would take too long for us to try and work out all the 4 digit numbers. So next we worked out a system...
We started at the top and worked out all the 2 digit numbers that make 15 which were
14 + 1; 13 + 2; 12 + 3; 11 + 4; 10 + 5; 9 + 6; 8 + 7; 7 + 8; 6 + 9; 5 + 10; 4 + 11; 3 + 12; 1+ 14;
Then we looked at next row down and worked out that we couldn't have 1 + 14 and 14 + 1 because we we couldn't use 0 so nothing adds up to 0. We took a pair of numbers each and worked out some of the group of 3 numbers which were:
|9 + 6||8,1,5||7,2,3||6,3,2||5,4,3||4,5,1|
|5 + 10||4,1,9||3,2,8||2,3,7||1,4,6|
|12 + 3||11,1,2||10,2,1|
|6 + 9||3,3,6||2,4,5||1,5,4||4,2,7|
|11 + 4||10,1,3||9,2,2,||8,3,1|
|8 + 7||7,1,6||6,2,5||5,3,4||4,4,3||3,5,2||2,6,1|
|7 + 8||3,4,5||5,2,6||6,1,7|
|10 + 5||9,1,4||8,2,3||7,3,2||6,4,1|
|3 + 12||1,2,10||2,1,11|
|13 + 2||12,1,1|
|4 + 11||3,1,10||2,2,9||1,3,8|
And from that we were able to do the exact same to work out the four
numbers which are:
2221; 8111; 4122; 4211; 5212; 3211; 5211; 4122; 7112; 5114; 3213; 3123; 7112; 2131; 7112; 7223; 5211; 2214; 2311; 8231; 1312; 6113; 1127; 1118; 4212;
We really enjoyed the challenge and our (something? brains? hands? minds ?) hurts after it but in a good way.
We really needed to keep a growth mindset.
This has been explained very well but now have a look at the ones I've put in italics (and underlined) what do you think about them?
We also had a number of solutions sent in from Peak School in Hong Kong
I found that all of my solutions always had a 1 in the bottom row, and the
total of all the numbers in the bottom row was always an odd number.
Victoria K & F wrote:
These are our solutions:
There has to always be a 1 in the bottom row.
In the bottom row will always be a number repeated twice.
The bottom row must equal an odd number.
The second to bottom row must equal 11, 12 or 13.
There must be a combination of odd and even numbers in every row.
I found out 9 different ways to get 15 using different numbers.
Sophie and Dorika wrote:
We think that the bottom line has to add up to an odd number.
We also found out that there has to be a one in in the bottom row.
The middle line can't have a one in it.
The second to bottom row will equal to 11, 12, 13.
On the bottom row a number will always be repeated twice or three times.
There are only 4 pairs of numbers that can be used in the second row.
We combined your idea and we did our own version using decimal points
6 3 3
4 2 1 2
2.5 1.5 .5 .5 1.5
1.25 1.25 .25 .25 .25 1.25
.125 1.125 .125 .125 .125 .125 1.125
Chloé, Holly and Anna wrote:
We found these solutions by starting from the top row and working our way
to the bottom:
We found some rules after finding the solutions:
-The bottom row must equal an odd number (7, 9, 11)
-The second to bottom row equal 11,12 or 13
-On the bottom row there will always be a number repeated twice
-There has to be be one in the bottom row
Thanks for reading!
Jihun from Dong Sung Elementary School in South Korea sent in the workthat had been done:
Well done all of you. It was very interesting reading about your methods and the things that you found out that had to be. Keep up your good work.