December 8, 2023

It’s the beginning of term, so let’s hear it for King’s Maths School, a state sixth form college in London, which topped this year’s A-level rankings: 69 per cent of A-levels taken by its students were A*, and 92 per cent were A or A*. Chapeau!

The school was founded in 2014 by King’s College London, and caters for the mathematically gifted. Each year has about 70 students, of whom 1 in 4 has parents with no history of higher education. About 1 in 3 students progresses to Oxford or Cambridge, a higher proportion than any other school.

The school’s mission includes maths outreach and enrichment for younger children. For example, during term time it posts a weekly mathematical challenge online aimed to intrigue and inspire children aged 13-16.

Today’s puzzle is one of these challenges. It was devised by King’s Maths School alumna Kirsty Land.

The amazing word machine

The following rules transform one word to another

  1. Add any vowel to the start of a word. i.e. MAZE –>AMAZE.

  2. Add any consonant to the end of a word. i.e. CARD –> CARDS.

  3. Delete two or more consecutive vowels. i.e. PLEASE –>PLSE.

  4. Delete two or more consecutive consonants. i.e. STRING –> SING, RING, ING or STRI.

  5. Double the entire word. i.e. AYE –> AYEAYE.

Note that any string of letters is considered a word. The “empty word” is a word with no letters, which we call “nothing”.

(a) Starting with LEAD, find a way to make GOLD

(b) Can all words disappear to nothing, that is, starting with any word, it is always possible to apply the above rules in such a way that you will get to the empty word? Prove the claim, or disprove it.

(c) Can you create any word from nothing, that is, starting with the empty word can you create any target word using only the rules above? Prove the claim, or disprove it.

I’ll be back at 5pm UK with the solution. PLEASE NO SPOILERS.

UPDATE: To read the solution click here

The idea behind King’s Maths School is to nurture children with an aptitude for maths, and widen participation in maths degrees and careers. When it opened in 2014, it was the first dedicated maths school in the country. Now there are seven, sponsored respectively by the universities of Exeter, Liverpool, Lancaster, Imperial, Cambridge and Leeds. Four more maths schools will open in the next few years.

If you enjoyed today’s puzzle and are doing your GCSEs, why not consider applying to your local maths school for sixth form!

To get in to King’s Maths School is hard: more than ten students apply for every place. Campus is in Lambeth, south London, but students come from across the city and some even commute from beyond the M25.

All students take Maths, Further Maths and Physics A-levels, and either Computer Science or Economics to AS-level. The school uses PhDs at King’s College as mentors for the students. It also provides professional development for maths and physics teachers in other schools.

To read more about King’s Math’s School check out its website.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.

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