Find out the answer to the Everything is Mathematical Curious Numbers puzzle number 17, published in The Times on Friday 28 September.

Which of the following numbers is not happy?

19, 23, 25, 28, 31

Correct answer:

25 is the only number in the sequence that is not a so-called “happy number”.

A happy number is a positive number which, if you replace the number by the sum of the squares of each individual digit and then continue repeating the process, will eventually become 1.

For example 19:

1² + 9² = 82

8² + 2² = 68

6² + 8² = 100

1² + 0² + 0² = 1

Find out the answer to the Everything is Mathematical Curious Numbers puzzle number 16, published in The Times on Thursday 27 September.

What is the missing calculation in this sequence?

2² = 1+3
4² = 1+3+5+7
8² = ?Correct answer:

8² = 1+3+5+7+9+11+13+15. The result of squaring a number can be arrived at by progressively adding consecutive odd numbers.

See Friday’s edition of The Times for another Curious Numbers puzzle.

There is a cookery concept that every good recipe needs only three elements to combine together to make a tasty dish. However, there is a debate amongst academics who are interested in an opposite problem: The Incompatible Food Triad. This puzzle aims to find three ingredients such that any two of them will go well together, and yet all three will not.

Mathematician George Hart was intrigued by this puzzle and documented a list of his solutions. In order for the three ingredients to be considered a solution, each of its three pairs must be something people would want to eat.

Hart gave an example where a = espresso, b = milk, and c = lemon juice. Each pair combines favourably: a + b = latte, a + c = are often served together, and b + c = paneer cheese. However, a + b + c is a curdling combination that doesn’t go well together at all!

He attended MIT and has a degree in Mathematics, Computer Science, and Electrical Engineering. Furthermore, he received an MA and a PhD in Applied and Computational Mathematics from Princeton University. In recent years he has focused his research on the application of time-frequency methods and sparse signal processing.

His interest in both music and maths led him to try and solve the problem of how to create a musical score with no pattern. Using the work of mathematician Évariste Galois and a concept known as Golomb Rulers, he created a piece specifically for the piano; it has been described as the world’s ugliest piece of music!

At University College Dublin, he founded the Complex & Adaptive Systems Laboratory, where biologists, geologists, mathematicians, computer scientists, social scientists and economists work on global challenges through computational modelling.

It is widely recognised that the right region of the brain is primarily involved in basic quantity processing and the left region is involved in more precise numerical operations.

However, it wasn’t known whether the two hemispheres could work together to improve maths ability; a study by researchers at the Dallas Centre for Vital Longevity, Duke University, and the University of Michigan, has been able to prove that they can, and they do.

The researchers found that during an arithmetic task, the communication between the left and right hemispheres increased significantly. They also saw that those who had shown the strongest connection between hemispheres were the fastest at solving the subtraction problems.

These findings suggest that inefficient communication between the two hemispheres may contribute to dyscalculia, the numerical equivalent to dyslexia. Armed with this knowledge, training could be put in place to encourage connectivity between the two sides of the brain, therefore stimulating maths development.