Challenge Level

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:

making 15 | making | the | two | totals | |||

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;

We really enjoyed the challenge and our (

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

We also had a number of solutions sent in from Peak School in Hong Kong

Alyssa wrote:

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:

Rules:

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.

Mathias wrote:

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.

Extension:

We combined your idea and we did our own version using decimal points

15

9 6

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.