# Matchsticks and n-dimensional hypercubes

Here’s an addictive maths challenge for you to try.

It’s separated into four stages:

• blue (easy);
• green (medium);
• yellow (hard); and
• orange (very hard).

k = 3 in each example.

# Will Smith on Talent, Skill & Success

“Talent, you have naturally. Skill is only developed by hours and hours and hours of beating on your craft” – Will Smith

I read an interesting article in The Conversation this morning, in which, author Kevin Donnelly claimed that the recent success of Shanghai’s students in international examinations such as PISA and TIMSS was owed to the “chalk and talk” teaching method that’s so popular in Chinese schools.

I have a different view. I think that their success was owed to one main thing: study-hours. Typically, school students in China spend ridiculous amounts of time practising for those tests, which usually translates into excellent scores on examination day. Here’s why.

Ericsson’s 10,000-hour rule states that on average, people become world-class ‘prodigies’ at a particular skill (such as playing a sport, chess, or an instrument) after spending about 10,000 hours practising that particular skill. The 10,000-hour rule was made famous by Malcolm Gladwell in his excellent book Outliers, who illustrates the rule using Bill Gates, Bill Joy, the Beatles and famous chess players as examples, all of whom spent about 10,000 hours practising before they had a major breakthrough on the world stage.

The notion that greatness comes with tenacious practice seems obvious to most adults. However, it seems less obvious to most children.

High-achieving students spend more time on their homework assignments. When the teacher doesn’t set any homework, the high-achieving students re-read the textbook and/or re-write their notes, allowing them to clock up extra study-hours before their final examination. Students with more study-hours, in my experience, really do get higher grades.

We can estimate the number of study-hours a student gets per subject during Years 11 and 12. Five Chemistry lessons per week totals 300 hours. Doing 3 hours of homework every evening (averaging 45 mins per subject) equates to another 300 hours in two years. Students who study each subject for 50 minutes a day during the school holidays will clock up an extra 80 study-hours. Weekly tutoring could add another 160 hours, and last-minute revision lectures (e.g. such as those from TSFX) could add another 10 hours.

Students who ‘cram’ for three weeks right before the exam for 8 hours a day, 6 days a week earn an extra 36 hours per subject.

First, we can see that sustained, deliberate practice throughout Years 11 and 12 is clearly the best way to clock up extra study-hours, and thus maximise your examination score at the end of the year. Second, we notice a huge disparity in the amount of time that students might devote to their studies in Years 11 and 12. The disparity in study-hours is about as large as the range of test scores you might find in a class: 42% to 90%.