What happens if we add one more 1?
What is 1111111111 × 1111111111?
Of course, you can type this into a calculator, but first try to follow the pattern and work out what the answer might be… then check it with a calculator.
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What am I?
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How many ways can you partition 4?
How many ways can you partition 5?
How many ways can you partition 6?
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What percentage of the 10,000 men were still there when they reached the bottom of the hill?
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This is a UKMT JMC (Junior Maths Challenge) question. I’ve been using it with my students, who applied to St Paul’s Girls’ School, in the recent 11+ entrance exams.
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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
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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The Ancient Egyptian Rhind Papyrus dates back to around 1550 BC and is full of mathematical ideas and puzzles. Not surprisingly, it has a section about calculating the slopes of pyramids.
I particularly like that it opens with the statement: “Directions for Attaining the Knowledge of All Dark Things”. That’s quite a way to describe mathematics.
The papyrus has a great deal about “Egyptian fractions”, which means that every fraction has to be described in terms of other fractions which have the numerator 1.
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The mathematical term “googol” was invented in 1920 by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. A googol is 10100, which means it is written as 1 followed by one hundred zeroes.
The fact that it can be written in such a compact form, 10100, is deceiving, because it represents a phenomenonally gigantic number of mind-blowing proportions. A googol is about one hundred billion billion times bigger than the number of particles in the visible universe (1080).
Although the company and search engine Google is spelt differently, it based its name on the huge number googol, because its ambition was to provide users with huge amounts of information.
What is googol squared?
What is √(googol)?
Pick any 4 digit number (as long as the digits are not ALL the same).
Put the digits in ascending order and descending order to create two numbers.
Subtract the small number from the big number, to create a next stage number.
Then repeat the process with the new number
Eventually you end up with 6,174.
So for a number to be happy, just take the digits, square each digit and add all the squares to create a new number. Then repeat the process with the new number, and continue until you end up with the number 1 or find the numbers stuck in a repeating loop that does not contain 1.
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