# It’s the Friday Puzzle!

75

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.  Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

## 75 comments on “It’s the Friday Puzzle!”

1. Pygmalion says:

took me 2 minutes 4 seconds

• Eddie says:

Same here!

• SimonP says:

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

• Eddie says:

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

• Manley says:

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.

2. erlendaakreE says:

1972!

3. Al says:

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.

4. Liam says:

Got it.
Nice to have an easy one once in a while!

5. Morgan says:

One!

(But it’s been subdivided.)

• Jimbo says:

I missed that one!

6. PhysicsChris says:

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

• nanda says:

yeah. no so simple.

7. Jerry says:

8. Sean Walker says:

• nanda says:

true

9. Mike Hitchcock says:

Hmmm…the sum of squares, eh…

10. Steve Jones says:

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…

11. unice says:

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

12. Calamitous chocky says:

there are 2… the 2 guys playing the game

13. @davebakedpotato says:

I first read that as ‘cheeseboard’.

14. Bear Grylls says:

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.

15. Alex says:

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 🙂

16. RobHes says:

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

• Berhard says:

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…

17. 30 seconds trying to figure out whether I misread the question, then about a minute working the answer out and checking it.

18. cimddwc says:

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)? 😉 Then I got the pattern pretty quickly and got the solution in, uhm, about a minute or a little more.

19. Edgar says:

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

20. Mickey D says:

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

21. Magnus Meyer says:

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

• Berhard says:

Danm, i did not even consider google search… 😉

22. fluffy says:

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

23. 30 seconds to do the math.

24. Roland says:

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

25. AMWhy says:

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!

26. Timdifano says:

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

• Engywuck says:

Same here 🙂

27. mittfh says:

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!) 🙂

28. Driffles says:

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

29. Manbat says:

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.

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

can you solve THAT puzzle?

32. Unimatrix says:

“Squares” is the magic word. 🙂

33. Steve says:

“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.”

34. 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.

35. Himanshu says:

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

• Anonymous says:

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

36. deepfield says:

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

• Lazy T says:

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

• Engywuck says:

Challenge accepted 🙂
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…

37. frederick says:

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

38. thomashpaine says:

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.

39. Knut-Sverre says:

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 8×8 chessboard” (my emphasis).

• NoAstronomer says:

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.

40. Dannie says:

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

41. Sari1967 says:

Simple puzzle pah!

42. . says:

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

43. h says:

2 mins hope it is right

44. Jan says:

3 mins. no pen and paper

45. NoAstronomer says:

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

46. Dee says:

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

47. majikthijs says:

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.

• Lazy T says:

Me too, so we are both wrong.

• matt, but not matt or the other matt says:

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

48. Bryn says:

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

49. John Loony says:

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

• Engywuck says:

wtf? Albeit we shouldn’t discuss answers.
How did you find this solution??

50. Khalid Marzook says:

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.

51. davemabus says:

@theorwellprize

TAM 9 – atheist revolution? stupid sh&theads

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

52. Noel says:

53. Anonymous says:

it took me 7 seconds, no joke

54. Anonymous says:

About 20 seconds for me – good question.

55. Anonymous says:

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.

56. 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