Science

Did you solve it? 2020 in numbers


Earlier today I set you the following problems:

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?]

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, almost everyone born on Jan 1 2020 (about 360,000 people) will be older than someone born in 2019 – all it takes is one birth in French Polynesia between 10pm-midnight on Dec 31 for almost everyone else born on Jan 1 2020 to be older than that 2019 birth. I think a French Polynesian birth in that two hour window is a fair assumption, based on this site.

(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.

3.1) Fill in the blanks in the following ‘countdown’ 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.

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

Solution

I received dozens of answers. I really liked this 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.

((10 x 9 x 8 x 7 x6)/5+(4 x 3))/(2+1) = 2020

(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)

If you want to revel in more 2020 number patterns, including Pythagorean triples, palindromic primes and more, check out Inder’s paper 2020 in Numbers: Mathematical Style. It’s amazing!

Thanks everyone for taking part. I’ll be back in two weeks.

Meanwhile, Happy New Year – and don’t forget to include Mikko’s operators when you chant the countdown tomorrow night.

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.





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