Question

By joining dots together, how many squares can you draw on a grid measuring 4 dots
by 4 dots?
what about a 5x5? Can you generalise for any size grid?

Answer 1

This is again just a challenge problem for those how wish to think

Answer 2

I am not sure about the generalisation for this :-)

Answer 3

\[s^2+(s-1)^2+(s-2)^2...(s-s)^2\]

Answer 4

4x4 ----13 squares

Answer 5

4*4= 20 squares

Answer 6

Oh oops sorry

Answer 7

5x5 ------ 24

Answer 8

it can be like this:
. .
. .
or
.
. .
.

Answer 9

I guess you miss all the sideways ones harkirat

Answer 10

there is 1 4*4, 6 3*3, 13 2*2

Answer 11

So the formula for the normal oriented ones would be
\[(s-1)^2+(s-2)^2...(s-s)^2\]
Where s is the number of dots per side

Answer 12

9+3+2+1=15 not right..

Answer 13

wow 9+4+1+0=13

Answer 14

Lol hold you horses

Answer 15

yeah that is right, I see, than you need to add the sideways

Answer 16

I can't see how to get 20 squares though

Answer 17

yes i missed the sideways ones !!!

Answer 18

for the 4*4 there is 2 3*3 and 4 2*2 sideways

Answer 19

how much is there for the 5*5?

Answer 20

well there are 20 :)

Answer 21

Oh wait I got 20 sorry

Answer 22

for the 5*5 there are 9 2*2 sideways, 4 3*3 and 2 4*4

Answer 23

so it will be (s-2)^2+(s-3)^2 +2 sideways

Answer 24

you can rotate it

Answer 25

ok Andras, here's one for u

A man buys 100 metal balls from a store. They r all the same shape and size and packed 10/bag.
BUT by mistake one bag contains balls which are all less by the same amount of weight as compared to the weight desired and available in other bags.

Shipment has to move out in 2 minutes when this discrepancy is noticed-- from the total weight of the shipment. However, an employee wins a reward from the boss by finding out the wrong bag by just one weighing (and it is not by fluke). Can u explain how ?????

Answer 26

I posted a new one, now I go and make myself some food

Answer 27

alright good question andras

Answer 28

thanks :-)

Answer 29

This is not the answer but it holds true through s=5
\[(s-1)^2+(s-2)^2...+(s-s)^2\]
+\[(s-2)^2+(s-3)^2...+(s-(s+1))^2+(s-2)\]