A simple one this week….. how many squares are there on an 8×8 chessboard?

As ever, please do NOT post your answers, but do say whether you think you have solved it and how long it took.ย Solution on Monday.

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took me 2 minutes 4 seconds

Same here!

Took me 3 minutes 24 … You seem a bit quick!

We may have rushed a little, but we’re fairly confident…!

Nice!

I wanted to say ‘A chess board features two squares. One plays as white and the other as black.’ but I quite like chess.

I will say that I worked out the formula almost immediately, but am slightly drunk, so took almost all of my 2 minutes and 4 seconds doing simple arithmetic.

1972!

Bit of a counting exercise, isn’t it? Figured out the route to the answer in a couple of seconds. More time spent checking I’d got them all.

Got it.

Nice to have an easy one once in a while!

One!

(But it’s been subdivided.)

I missed that one!

I think you have lied. It is not so simple ๐

yeah. no so simple.

I saw one answer immediately. Then, I saw the correct answer!

First I had an answer. Then I had an improved answer. Then I saw a pattern and had the right answer.

true

Hmmm…the sum of squares, eh…

In case some people might find chess a little too complicated, to make it easier I would suggest thinking how many squares are there in a draughts board…

I think i know it. Took me a couple of minutes…

there are 2… the 2 guys playing the game

Hee hee ๐

I first read that as ‘cheeseboard’.

About 3 minutes, being methodical.

Thought of captain obvious answer for 2 seconds, then realised what it was asking. Thought I was in for lots of tedious counting, then noticed a pattern by the second set of squares. Grabbed calculator. ?????, Profit. Probably 2 mins.

Worked out the pattern quite quickly so was able to work it out for a chessboard, glad the board wasn’t much bigger else I would have resorted to using a quick bit of code to do the work ๐

30 seconds “brute forcing” it, then spotted the correct way of solving it – one minute doing the mental arithmetic and double-checking.

Dito…

However presumably started with a short cut…

However, the solution depends on how are the squares defined… if all squares are allowed that may be definded between all crossing points.. i would have to count again…

30 seconds trying to figure out whether I misread the question, then about a minute working the answer out and checking it.

I suppose we’re supposed to align the squares to the 8×8 small black and white squares and not break it down to the size of atoms or even space quantums (if any)? ๐ Then I got the pattern pretty quickly and got the solution in, uhm, about a minute or a little more.

About 5 minutes. I-m not that good at math.

Think I got it in half a minute, but reading the comment I might have to recount…

cba to do the calculation. one google search 1.367 secs ^^

Danm, i did not even consider google search… ๐

Had the obvious incorrect one instantly, had the less-obvious and hopefully-correct one pretty quickly.

30 seconds to do the math.

Wondering if on Monday, the obvious square will be forgotten ๐

1 second to get the wrong answer, about 5 seconds to think of a method, about 45 seconds to add my numbers together in my head. About an hour more of work before I can look ata piece of paper ad confirm it!

Took about 2 minutes or so to derive and generalise the pattern, then another minute to do the maths.

Same here ๐

I knew immediately that the answer wasn’t the obvious one – a little playing around with a relevant sized grid, one sum, and I arrived at what is probably the answer Richard’s looking for.

The nice thing is that you can easily scale up or down for boards of different sizes without needing to count (as long as you know the grid size!) ๐

Pretty easy if you had your times tables hammered into you by your parents as a child, like me.

30s if I’m right, until monday morning if I’m wrong

About 1 minute to spot the pattern, and then 30s to do the sums.

my answer is hidden in the crossword style clue – “Luxembourg sounds like its lost purpose” –

can you solve THAT puzzle?

“Squares” is the magic word. ๐

“Oh, that’s easy. There’s… wait… what about… so that’s… but they could also… I’m gonna need a piece of paper for this.”

Interesting. I was delighted to spot a pattern right off that made my maths somewhat easier. About a minute. I’ll see on Monday if I’ve overlooked anything important.

Very quickly because did this once in a maths class. Didn’t remember the answer but remembered n(n+1)(2n+1)/6! ๐

Hey, Richard said DON’T post the answer…. :p

How about how many RECTANGLES are there? that would have been much harder!

1296, using the same principal as for the squares. I didn’t count them myself.

Challenge accepted ๐

I summed up rectangles for half an hour and find an astonishing simple solution! In a grid with 8×8 squares (chessboard) the lines may outline 1296 different rectangles. The formula I found is

Sum of n^3

with n from 1 to 8

= 1296

I systematically summed up all the rectangles with the basis of 1, add those with 2 and so on…

The formula for arithmetic series is helpful here. Please correct me if I’m wrong. I finally calculated a total of

Sum of 2*n*n*n/2

with n from 1 to 8

which equals Sum of n^3.

Now it’s not that hard to calculate the number of rectangles even for a 10×10 board…

Simple formula, 30 seconds. However, most chess boards have a square border, so perhaps we should add 1 to the answer ๐

I’m sure there’s an elegant math solution… I set up a representation of a board in Excel and set up some formulas to calculate all the iterations. I think I got it right. Took about 5 minutes.

Easy. There are 8 x 8 = 64 squares on a chess board. It is of course possible to draw a whole lot of new squares along the lines of the existing ones, but that is not the question here; it reads “how many squares ARE THERE on an 8ร8 chessboard” (my emphasis).

I actually like this answer. Should it prove to be the intended answer on Monday I’ll have no problem claiming to have known it all along.

Got the “technique” instantly, Just took a couple more minutes to actually calculate.

Simple puzzle pah!

8*9*17/6 = 12*17 = 204?

2 mins hope it is right

3 mins. no pen and paper

10 minutes or so, working on and off. Yes I had to use a pen & paper.

It took about a minute to figure out the maths, then ~10s ๐

about 10s to spot the pattern, not gonna bother to work out the number: I can wait until Monday and let Richatd do the number crunching.

Me too, so we are both wrong.

Help ! Whats a “square” ? See my problem:

http://dict.leo.org/ende?lp=ende&lang=de&searchLoc=0&cmpType=relaxed§Hdr=on&spellToler=&search=square

The answer does change depending on what kind of square you mean, doesn’t it.

I just started counting all of then and then got frustrated and googled it the answer is: 0

The square root of the sum of the cubes of the three consecutive integers from 23 upwards.

wtf? Albeit we shouldn’t discuss answers.

How did you find this solution??

I knew it straight away, not because I’m smart (I’m not even close to being that) but because I took it in college.

@theorwellprize

TAM 9 – atheist revolution? stupid sh&theads

http://freethinking.sotoman.info/index.php?topic=1995.msg10504

Took about .068seconds to get the answer multable times. Thanks google.

it took me 7 seconds, no joke

About 20 seconds for me – good question.

Caught the pattern quickly but had to prove to myself that it didn’t break down in actual application. Hey what can I say , I’m slow.

i know the answer 2 sec i see the answer. . . . . 2 triangle and your can brake that triangle f u remove 1 circle in the right side grrr