Can you solve it? 2020 in numbers

The new year deconstructed, and a prize challenge

UPDATE: solutions and results now up

It’s almost the New Year, and – numerically speaking – I’m excited. Not only is twenty-twenty already a bona fide word in the dictionary, but once a month next year there will be a moment in the evening when the time is:

20/20/20/20/2020

(hours/minutes/seconds/day/year)

I know! Peak vigesimal! What a score! Let’s celebrate with some puzzles:

1) How can someone born in 2020 be older than someone born in 2019?

[Follow up question: roughly how many people will fall into this category this year? That is, how many babies born in 2020, if any, will be older than at least one person born in 2019?]

2) Imagine 2020 is not a year but a rugby score, as I’ve scrawled below. This score spells out a word. Can you work out which one?

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3.1) Every year in this column I try to find the most attractive equation that counts down to the new year. In other words, fill in the blanks in the following equation so it makes arithmetical sense:

10 9 8 7 6 5 4 3 2 1 = 2020

You are allowed to use any of the basic mathematical operations, +, –, x, ÷, and as many brackets as you like. An answer might look something like (10 – 9 + 8) x (7 – 6 – 5)/(4 + 3 + 2 + 1) = 2020, but not this one since the equation is incorrect.

There are many solutions. I’ll give a copy of my puzzle book So You Think You’ve Got Problems? to the solution I think is the most elegant. You can either tweet me or email me your equations.

3.2) The numbers guru Inder J Taneja, a retired maths professor from Brazil, alerted me recently to a new New Year challenge: how to create the year using a single digit. For example, here is how you make 2020 using only 9s.

(9 + 9) × (99/9 + 999)/9 = 2020

Can you make 2020 using only 1s? Or using only 2s? Or using only any one of the other non-zero digits? The rules are that you cannot use any of the digits more than ten times in each of the equations. You can use all the basic operations, brackets, exponentiation, i.e. you can use a term like 22, and (as shown above) you can concatenate by putting digits together. At least one equation is possible for every digit from 1-9.

If you like patterns like this, do check out Professor Taneja’s treasure trove of numerical curiosities. He says: “Whenever I see a number anywhere, it has now become my natural instinct to search for patterns in that number. I spend time on this aspect because I like it. To me it is similar to what art is to an artist and what meditation is to a yogi. The appealing aspect is the mesmerising power of multiple permutation combinations which are possible, which makes me realise the incredible power of the universe and keep me grounded.”

Happy New Year everyone!

Meanwhile, NO SPOILERS

I’ll be back at 5pm UK time today with the solutions.

UPDATE: solutions and results now up.

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My latest book is So You Think You’ve Got Problems?, a compendium of 150 puzzles and the stories behind them. There are logic puzzles, word puzzles, lateral-thinking puzzles and much more. If you enjoy this column, I promise you will enjoy my book.

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.

Contributor

Alex Bellos

The GuardianTramp

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