Well done to everybody who had a go at this task. By my calculations, there are over a hundred possible solutions for each of Challenge 3a and Challenge 3b, so it's not surprising that nobody has sent us a full solution yet! If anybody does have any more solutions that they'd like to share with us, please email
us.
Most children correctly worked out the diagonal numbers for the spiral going up to 144. Arlo from South Harringay Primary School in England sent in this picture of the spiral:
Challenge 2 was slightly more difficult, and some children made mistakes with calculating the totals for each three numbers. The children from Stourport Primary Academy in the UK correctly found the ten totals and noticed a pattern between them:
Zac from the UK found 52 solutions for Challenge 3a and 84 solutions for Challenge 3b, but unfortunately some of Zac's numbers from Challenge 2 weren't quite right. Take a look at Zac's full solution to see their reasoning. How might Zac change some of these solutions to use the correct
numbers?
Ariel, Marlo and Robin from South Harringay found all of the totals in Challenge 2, but they also found a couple of extra totals that weren't made by adding groups of three numbers from the diagonal. They found these correct solutions for Challenge 3:
71 + 281 = 352
101 + 11 = 112
71 + 11 = 82
11 + 281 = 292
101 + 71 = 172
101 + 281 = 382
Thank you for sharing these with us! How can we be sure that this is all of the possible ways of completing Challenge 3 by only adding two numbers that end in the digit 1?
Shubhangee, the teacher of Viha, Abhiram, Eshann, Anirved, Arya, Rivaan, Miraya, Asma, Aprameya, Vibha, Rudraraj, Nithyashree, Adhrit, Kathir, Arnav, Arjun and Harshad from Ganit Kreeda, Vicharvatika, India, sent in their solutions to the task. They thought that there would be 75 solutions for Challenge 3a and 102 solutions for Challenge 3b. I agree with this
number of solutions for Challenge 3b but I think there are more solutions for Challenge 3a. Take a look at Ganit Kreeda's full solution to see their ideas.