Can you solve it? Nick Berry, Data Guy

Sad news to announce. Nick Berry, the British data scientist who wrote DataGenetics - one of the best and oldest popular mathematics blogs - has died aged 55 after a long battle with cancer.

Nick was a Yorkshireman who studied aeronautical engineering at the University of Southampton. He then moved to Seattle, where he worked as a data scientist for companies such as Microsoft and Facebook. He started DataGenetics in 2009 and he quickly garnered a huge following for his accessible articles on interesting topics in math, physics and computer science.

Nick had an excellent eye for good subjects, a gift for effortless explanation 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. Hero without zero

Write 1,000,000 as the product of two numbers; neither contains zeros.

(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 that she has a secret number less than 100.

She also confesses the following information: "The number is only describable by 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, due to the ambient noise at the party, you only hear the answer to one of the questions, which is "yes". What is Lucy's secret number?

3. Naughty math elves

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

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

This vandalism continues all night until there is only one number left.

I go back to the board the next morning and find the unique number on the board. Is that remaining number even or odd?

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

PLEASE NO SPOILERS

(And if you check out the Datagenetics blog, which I recommend, don't look for the answers to these riddles just yet!)

< p class="dcr-1vtk2mf">I put a puzzle here every two weeks on a Monday. I'm always on the lookout for great puzzles. If you would like to suggest one, email me.

I give school lectures on math and puzzles (online and in person) . If your school is interested, please contact us.