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# Maze 100

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### Pebbles

### Bracelets

### Sweets in a Box

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Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Hollie from Gresham Primary School offered the following general advice when tackling this task:

I have three strategies I used.

1) You can start by drawing a random line then add up mentally or write it down. However, if you're trying to get 100 don't go straight round the outline because it will be too small.

2) Add the numbers up as you go and make a note of totals when you get to corners. Then if you need to make the final answer bigger or smaller you can just go back to the last corner to change the route.

3) The main thing is even if you don't get it straight away is be creative, resilient and persevere. Don't forget to check your adding!!

What fantastic tips, Hollie, thank you.

Bonner Primary School sent in this commentary:

Thoughts before we started:

** Aarfin**: I think you have to use a lot of numbers to make 100.

Thoughts as we began:

Thoughts after 20 minutes

Jess and Suja from Harrisons School explained the way they approached the task:

To solve the Maze 100 problem we used a systematic approach. We started off by drawing all of the possible routes from the start to the end of the maze and colour coded them to make them clear. Then we added up the numbers along those route separately so we could find which one added up to 100. From finding all of the routes and adding them up it was easy to find out the
highest and lowest as we had all of the information ready.

Hugo and Josh, and Finn and Ben, also from Harrisons School, sent in very clear solutions. Here is Catrin and Abi's. It is not totally correct, but we thought it worth including as they worked hard to try to find all the possible routes through the maze (there are some comments underneath which will help you spot the errors):

Well done, Catrin and Abi. I think there are a few slip-ups in their solution:

- I wonder whether they have missed out one possible route;
- The totals of numbers 1, 2, 3, 4, 5 and 8 are not quite right, which affects the lowest possible total and means there may be another solution to the challenge of making 100 (!);
- I think in solution number 6, there is a 6 missing near the end (but the total is correct).

Sonja sent in a link to a video in which she talks through her findings.

She found two ways to make 100. She also found the lowest route of 37 and the highest route of 101. The video can be viewed at www.educreations.com/lesson/view/maze-100/23257143/?s=NXNLIp&ref=link

Here is an image of the two ways Sonja found of making a total of 100:

Here is an image of the routes Sonja found with the smallest and largest totals:

Well done, Sonja!

Isabelle and Takumi from Monarch Global Academy, USA; children at Cefnllys-Llandrindod County Primary School in Wales; Lea and Ayla from Torriano Primary School; Mariah from Stimpson Avenue Academy; Frida, Steven, Harsh, Yuha, Matthew and Zoe from Nord Anglia International School Hong Kong; Kaitlyn from St.Helen's Primary
School; Liam and Olivia from Millfields Primary School; Year 4 from Britannia Primary School; Bryon and Grace Kaiapoi North School in New Zealand; Jamie and James from Sheuchan Primary School in Scotland; Max from Dussindale Primary School; Leila, Amaya, Aoife, Saachi from North London Collegiate School; Advika
from Wimbledon Chase Primary School, Thomas, Cayden, Rudi, Emilia, Matthew and others from Hempland Primary and James from St Williams Primary School all sent in good solutions too.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?