At the start of term, let’s celebrate King’s Maths School, a state sixth form college in London, for topping this year’s A-level rankings. An impressive 69% of its students achieved A* grades, and 92% obtained A or A* grades. Well done!
Founded in 2014 by King’s College London, King’s Maths School caters to mathematically gifted students. With approximately 70 students per year, 25% of whom have parents without a history of higher education, the school achieves a higher proportion of students progressing to Oxford or Cambridge than any other school.
In addition to its academic achievements, the school is dedicated to maths outreach and enrichment for younger children. One of its initiatives is a weekly mathematical challenge aimed at inspiring and intriguing children aged 13-16.
Today’s puzzle is one of these challenges, devised by a King’s Maths School alumna named Kirsty Land.
The amazing word machine
The following rules can transform one word into another:
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Add any vowel to the start of a word. For example, MAZE becomes AMAZING.
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Add any consonant to the end of a word. For example, CARD becomes CARDS.
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Delete two or more consecutive vowels. For example, PLEASE becomes PLSE.
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Delete two or more consecutive consonants. For example, STRING becomes SING, RING, ING, or STRI.
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Double the entire word. For example, AYE becomes AYEAYE.
Keep in mind that any sequence of letters is considered a word. An empty word is a word without any letters, which we refer to as “nothing.”
(a) Starting with LEAD, find a way to make GOLD.
(b) Can all words disappear into “nothing”? In other words, can you always apply the rules above to any word and eventually reach the empty word? Prove or disprove this claim.
(c) Can you create any word from “nothing”? In other words, starting with the empty word, can you reach any target word using only the rules mentioned above? Prove or disprove this claim.
I’ll reveal the solution at 5pm UK time. Please, no spoilers!
King’s Maths School aims to nurture students with a passion for mathematics and promote participation in maths degrees and careers. When it opened in 2014, it became the first dedicated maths school in the country. Since then, six more schools have been sponsored by the universities of Exeter, Liverpool, Lancaster, Imperial, Cambridge, and Leeds. Four additional maths schools are set to open in the coming years.
If you enjoyed today’s puzzle and are currently studying for your GCSEs, why not consider applying to your local maths school for sixth form?
Getting accepted into King’s Maths School is highly competitive, with more than ten students vying for each place. The campus is located in Lambeth, south London, but students come from all across the city and even commute from beyond the M25.
All students at King’s Maths School take Maths, Further Maths, and Physics A-levels, along with either Computer Science or Economics at AS-level. The school provides PhD mentors from King’s College to support the students and offers professional development opportunities for maths and physics teachers from other schools.
To learn more about King’s Maths School, visit their website.
Every two weeks on Mondays, I share a puzzle here. I’m always on the lookout for great puzzles. If you have any suggestions, feel free to email me.
I also offer school talks about maths and puzzles, both online and in person. If your school is interested, please get in touch.
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