– puzzle and solutions ©Alex Bellos (The Guardian)

) 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?]

Solution: If someone is born, say, at 1am in the morning of January 1 2020 in Sydney, then everyone born in the UK in the afternoon of December 31 2019 will be younger than them but born the previous year.

In fact, the number of people born in 2020 who are older than someone born in 2019 is going to be in six figures. About 360,000 people are born every day. (Most in Asia). A child born in French Polynesia between 10pm-midnight on Dec 31 2019 will be younger than all the Jan 1 2020 births until that moment, i.e until 6pm in Beijing, 3.30pm in Delhi, and so on. A fair estimate is probably about half of 360,000.

(Hat tip to the reader who said that anyone born in 2020BC will be older than anyone born in 2019AD)

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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Solution Wipe a tear from your eye. The word is ONION. Rotate the score by 90 degrees anticlockwise and you’ll see.

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.

I also said that I would send a copy of my book to the solution I found the most elegant.

Solution

Thanks to everyone who took part. I received dozens of answers. I really liked the following one: not for its elegance but for it’s chutzpah. You multiply the first five figures together to overshoot the target by as far as possible, before dividing to get to the green.

(As suggested by Chris Duffy and Colin Beveridge (@icecolbeveridge))

The most elegant, however, I felt was this one by Mikko Harju from Finland. Only two sets of brackets, and only two of the possible four operators. Congrats Mikko, a book is on its way to you.

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

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.

Solution

Here are Inder’s solutions:

  • (1 + 1) × (11111 − 1)/11
  • 2 × (2 × (222 + 22) − 2)
  • 3 + (3 + 3) × (333 + 3) + 3/3
  • 4 + (4 + 4) × (44 − 4)
  • 55 + 55 × (5 − 5 × 5) − 5
  • (6 − 6/6 )× ((6 + 6)/6 + 6 × 66 + 6)
  • 77/7 + 7 × (7 × (7 × 7 − 7) − 7)
  • (8 × (8 × 8 × 8 − 8) + 8) × 8/(8 + 8)