Can you solve it? Nick Berry, data dude

Some sad news to report. Nick Berry, the British data scientist who wrote DataGenetics – one of the best and longest-running maths popularisation blogs – has died aged 55 after a long battle with cancer.

Nick was a Yorkshireman who studied Aeronautical Engineering at Southampton university. He later moved to Seattle, where he worked as a data scientist for firms including Microsoft and Facebook. He started DataGenetics in 2009 and it soon gathered a huge following for its accessible posts about interesting topics in maths, physics and computer science.

Nick had a great eye for good subject matter, a gift for effortless explication and a continual joy in the subject. He also liked a good puzzle. Today’s three challenges are taken from his blog, with permission.

1. No-zero heroes

Write 1,000,000 as the product of two numbers; neither of which contains any zeroes.

(You may be interested to know that 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000)

2. Lucy’s secret number

You are at a party and overhear a conversation between Lucy and her friend. In the conversation, Lucy mentions she has a secret number that is less than 100.

She also confesses the following information: “The number is uniquely describable by the answers to the following four questions:”

Q1) Is the number divisible by two?
Q2) Is the number divisible by three?
Q3) Is the number divisible by five?
Q4) Is the number divisible by seven?

She then proceeds to whisper the answers to these questions to her friend. Unfortunately, because of the ambient noise at the party, you only hear the answer to one of the questions. Knowing this one answer allows you to determine the secret number. The answer you hear is ‘“yes.” What is Lucy’s secret number?

3. Naughty maths elves

I write the whole numbers from 1-9999 (inclusive) on a huge chalkboard. Each number is written once.

During the night the board is visited by a series of naughty maths elves. Each elf approaches the board, selects two numbers at random, erases them, and replaces them with a new number that is the absolute difference of the two numbers erased.

This vandalism continues all night until there is just one number remaining.

I return to the board the next morning and find the single number of the board. Is this remaining number odd or even?

I’ll be back with the answers and solutions at 5pm UK

PLEASE NO SPOILERS

(And if you do check out the Datagenetics blog, which I recommend, don’t look straight away at the answers to these puzzles!)

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.