January 10, 2025
New Year traditions… and here’s my math-brainteaser one!
Happy New Year*, folks!
From the back end of each year and into the beginning of the following one, quite a few traditions are observed around the world. There’s “Catholic” Christmas on December 25 (that’s how it’s referred to in Russia!); there’s New Year (universally celebrated); and there’s Orthodox Christmas on January 7. In connection with the latter, there’s also another tradition of my own – my explaining why I tend to be quiet on these here blog-pages from late December to just after Orthodox Christmas, and why my “Happy New Year” greeting can seem, to some, several days late*: each day is a public holiday in Russia (this year: December 29 – January 8). But wait… There’s yet another tradition – also of mine: my festive mathematical brainteaser!…
The… necromancy of numbers, the elegance of equations… Yes – I am a mathematician by training, and yes – I never let you forget that early January of each year. But of course I don’t: for what better way is there to blow away the cobwebs of gloom brought on by the January blues?…
All righty. Explanations done. Let’s get to this year’s number-crunching riddle (actually – riddles)…
Top-level brainteaser
Using basic math (adding, subtracting, multiplying and dividing; brackets), turn “10 9 8 7 6 5 4 3 2 1” into the number of this year – 2025, neither changing the order of the numbers, nor combining them (e.g., 43+1+2).
For example, ((10 + 9) * (8 + 7) * (6 + 5) * 4) / 3 / 2 + 1 = 2091, but that’s no good as we need to get 2025.
Ok folks; did you work it out? Well done!
And for the next-level brainteaser – drop the 10…
2nd-level brainteaser
9 8 7 6 5 4 3 2 1 = 2025
Come on folks; thinking caps on (and answers in the comments please)!
Btw, here are some previous years’ festive New Year brainteasers, which may help you working out this year’s:
8 * (-7 + 6 * 5) * (4 * 3 – 2 + 1) = 2024
(8 * 7 * 6 + 5 – 4) * 3 * 2 + 1 = 2023
(10 * 9 + (8 – 7) * (6 + 5)) * (4 * (2 + 3)) + 1 = 2021
9 * 8 * 7 * (6 + 5 – 4 – 3) + 2*1 = 2018
Note: before the first numeral (for the top (full-10) brainteaser) you can place a minus, making it a negative number if you like.
It was working out this second-level brainteaser that I realized that 2025 is somewhat… unusual in terms of arithmetic. How come? Work it out yourselves! Meanwhile – onward!…
3rd-level
8 7 6 5 4 3 2 1 = 2025
4th-level
7 6 5 4 3 2 1 = 2025
Here, using just +, -, *, and / won’t get you to 2025; from this level downward (upward?), you can use factorials, raising to nth powers, radicals and other logarithms.
5th-level
6 5 4 3 2 1 = 2025
6th-level
5 4 3 2 1 = 2025
Here already you need to bring out the big guns of math like multiple factorials, sub- and super-factorials, and also primorials. Hints/tips/examples:
7! / 6 / 5 * 4 * 3 + 2 + 1 = 2019
6 / 5! * ( 4! / 3 )! + 2 + 1 = 2019
( ( ( 5 – √4 )! )!!!! ) !!!!! * ( ( 3 * 2 )!!!! ) + 1 = 2017
5# – sf(4) – 3 + 2 – 1 = 2310 – 288 – 2 = 2020
(5! – 4!) * Fibonacci(Fibonacci(3!)) + 2 * 1 = 2018
sf(4) * (3! + !2) + 1 = 2017
Sure, many of you will have eyes so glazed over by now that you can hardly see your own hand held up in front of your face. That’s ok; math is hardly everyone’s cup-of-tea. Regardless – onward!…
7th-9th levels
4 3 2 1 = 2025
3 2 1 = 2025
2 1 = 2025
Here you need special numbers – things like a Leonardo number, a Fermat number, the Fibonacci sequence, a Catalan number, a Mersenne prime, a Woodall number, the Lucas number, and/or more…
Past use of such integer sequences:
A Leonardo: L((L(3)) !!) + !( L(2 + 1)) = 1973 + 44 = 2017
Fermat and Fibonacci:
( 5! – 4! ) * F( F( 3! )) + 2 + 1 = 96 * 21 + 3 = 2019
( !( 3! ) – sf( M(2) ) ) * F( Fm(!1)! ) = ( !6 – sf(3) ) * F(6) = (265-12)*8 = 2024
Mersenne: -M(5) + M(4) + M(F(3!)) * (M(M(2)) + M(1)) = 2024
Now, still with us? Then… ->
10th-level
1 = 2025!
However!…
No cheating using previous solutions (so I won’t link them here!).
Now over to you, dear readers boffins!…
Like I say – answers in the comments please.
And that’s all for today folks.
Back soon!…
