Since I always fail my New Year's resolutions, this year, my New Year's resolutions are:
1. Make a new year's resolution
2. Fail my new year's resolution
Am I guaranteed to succeed? Guaranteed to fail? Something else?
Let weird(n) be the number of ways to write n as a + a + b + c, where n, a, b, and c are distinct positive integers. Is weird(n) an increasing function?
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A set of positive integers has sum 25. What is the biggest you can make the product of the numbers?
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Can you work out the area of the inner square?
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The pattern 123451234512345... is continued to form a 2000-digit number. What is the sum of all 2000 digits?
6000
7500
30,000
60,000
75,000
![UKMT (UK Mathematics Trust): [√ n]](https://images.squarespace-cdn.com/content/v1/580f3dddc534a5c144fe8a58/1600772690017-AF5AAN2C2RCFEV33MKQF/Screen+Shot+2020-09-22+at+11.24.25.png)
The notation [√ n] means the integer part of the square root of n. How quickly can you solve?
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Take away two matches to leave two squares.
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It is extraordinary that so much of the universe can be explained using mathematical equations. Indeed, it is often said that mathematics is the language of the universe. It is certainly the language of science.
In this clip, from a documentary in the American Nova series, the jazz musician Esperanza Spalding explains how maths is also at the heart of music. Pay attention to the way that numbers relate to musical intervals (an octave, a fifth and a fourth).
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