Milestones

Half term is here, and once Nicky was finished with her teaching today, we headed into Maidstone. First stop was a nice new (to me anyway) cafe where Jake and I had burger and chips, and Nicky had a fish finger sandwich. Then it was to the Golden Boot for Jake to have his feet measured and new shoes bought. Following a trip to the pediatrician earlier in the week, Jake now has inserts for his shoes to support his arches, and so we wanted to make sure that he had shoes that fit properly. He was wearing the inserts in his trainers as we went round town, and seems to get on fine with them.

As it's half term, so the half term projects have begun. Nicky has been helping with the science, which involves dissolving some solids into water, and then leaving them to see what happens when the water evaporates. The 'before' photos have been taken, and we will wait to see what happens. Hopefully, the cat won't find them and think that they're for him!

I've been helping with the maths project (well, ok I kind of did the project!). The challenge set was to pick four different digits from 1 to 9, and arrange them into a square. Then consider the sum of the two two-digit numbers made by reading across the rows and the two two-digit numbers made by reading down the columns. So, for example:

1 2

3 4

would be 12 + 34 + 13 + 24 = 83.

The question was - how many arrangements of the digits give an answer of 200?

The answer is 22 arrangements.

How did I work this out - well, basically by considering every possible arrangement, and seeing which ones gave an answer of 200.

How many arrangements are there? Well, the first step is to pick four digits. The number of ways of picking 4 from 9 is 9! / (5! x 4!) = 126.

For each of those 126 combinations, they can be arranged in the square in 4x3x2x1 = 24 ways. So, in total there are 126 x 24 = 3,024 possibilities.

(Although note that they come in pairs, as swapping the top right and bottom left digits makes no difference to the sum.)

I checked them all (using a spreadsheet) and there were 22 answers.

For the children in Jake's class who try to find them by trial and error, they will need to have a fair amount of staying power, given that there are so many to choose from, and less than 1% of the possible options give the right answer.

As to milestones, a couple to note today. Firstly, as a mini milestone, today is the 50th day of the year and my 50th blog of the year. Secondly, it is 100 days until Jake and I set off on our boys' adventure to the IOW.