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Maths Week: Your Saturday puzzle

Fancy another mathematics challenge? (And get the answer to yesterday’s puzzle.)

MATHS WEEK IS under way and, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!

Where are the Women in Maths?

Our series on the history of mathematics hasn’t featured women so far. That is a reflection of the times and the cultures, not on ability.

Women simply didn’t have opportunities to learn, or work in professions. That has thankfully changed and women are prominent now in all fields of maths.

However, some remarkable women have played a key role in the history of maths. Hypatia was a renowned mathematician in 4th-5th Century Alexandria. Unfortunately scapegoated for involvement in a political feud, she was murdered by a Christian mob.

When Newton’s great work, Principia Mathematica was published few across Europe fully understood it. Émilie Du Châtelet (1706 – 1749) read it, understood it and translated it into French.

Another French woman Sophie Germain (1776 – 1831) earned the admiration of the great
mathematicians Lagrange and Gauss.

Ada Lovelace (1815-1852) is credited with writing the first computer program.

Cork-born Alicia Boole Stott (1860–1940) was a self-taught mathematician who
excelled in four-dimensional geometry.

And, of course, Florence Nightingale.

What, Florence Nightingale?

The “Lady with the Lamp”?

Surely she was the founder of modern nursing?

Yes, she was but she was also an early proponent of hygiene and handwashing and the use of data to inform medical treatment.

Two key weapons in the battle against Covid19.

Born 200 years ago in Florence into a wealthy English family, Florence Nightingale was never content to fill the role that society at the time expected of a lady and defied her parents to become a nurse.

She went to the Crimean War to tend injured soldiers where she found that far more soldiers were dying of disease than wounds.

She gathered data about deaths in hospitals and her statistics pointed at poor sanitary conditions as the cause of high mortality rates. Concerned that politicians wouldn’t understand the statistics she developed visual displays similar to the pie chart that is common today.

This had a huge impact on the design and operation of hospitals resulting in a significant drop in death rates.

Famous for being the ‘Lady with the Lamp’ who nursed sick and wounded soldiers, her far-sighted ideas and reforms have influenced the very nature of modern healthcare.

Florence instigated the Wash Your Hands message in her Notes on Nursing in 1859. She transformed nursing into a respectable profession for women and in 1860, established the first professional training school for nurses.

She popularised the use of graphs and charts to convey information and now all important policy decisions are (or should be) informed by statistics. Florence died in London in 1910.

Her legacies of professional nursing training, hygiene and the use of mathematics and statistics in healthcare has saved countless lives and are critical in our current battle against this pandemic.

Can you help Florence to sort out the following data?

There were 30 soldiers in Florence Nightingale’s Crimean War field hospital all suffering from one or more of the ailments, dysentery, gunshot wounds and gangrene.

Of these, 12 had gunshot wounds and gangrene but not dysentery. Seven had no gunshot wounds but had gangrene and dysentery.

Four had gunshot wounds and dysentery but not gangrene.

No one had been shot that did not suffer from one of the other two ailments.

Only three patients suffered from only one ailment.

How many suffered from all three ailments? 

All puzzles are by Eoin Gill, the coordinator of Maths Week Ireland and director Calmast STEM Engagement Centre, Waterford Institute of Technology

Come back tomorrow for Sunday’s puzzle and the answer for today’s.  

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Friday’s puzzle: The Answer and Method

Rotating a die away from you through ninety-degrees three times will leave five facing up.

Two additional quarter turns to the right will leave two facing up.

However, if you first do two ninety-degree rotations to the right you will end up with four facing up.

Three ninety-degree rotations away from you will finish with five facing up.

In normal algebra, multiplication is commutative.

That is, ab = ba.

For example, 3×2 = 2×3

In Hamilton’s algebra, this property doesn’t hold.

In fact, ij = -ji.

This allows quaternions to describe rotations.

This changing of the rules was revolutionary.

It allowed Hamilton to create the quaternion algebra.

It also showed that it was valid in maths to create new systems with their own rules as long as these rules were consistent within that system.

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