#logic based question

72 messages · Page 1 of 1 (latest)

dense phoenix
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i have this 10x8 rectangle. how do i find the total number of squares that i can make inside of it

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weak coralBOT
glossy viper
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there's a formula for it

dense phoenix
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do u have it

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for me i got 64 squares

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but i know its wrong

glossy viper
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you mean the total number of squares in a 10 by 8?

dense phoenix
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yes

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the total nb of squares i can make in this grid

copper flame
dense phoenix
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80

copper flame
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and how did you find it

dense phoenix
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cuz its a 8 x10

copper flame
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great

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now how many 2x2 squares are in that grid

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try to find the pattern

dense phoenix
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hmmm

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20?

copper flame
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nope

dense phoenix
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40?

copper flame
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are you just guessing

dense phoenix
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hmm

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72?

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36?

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36

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it must be

copper flame
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how did you get those numbers

dense phoenix
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i counted on the grid and discovered a pattern

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and did 9x7

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u are very intellectual

copper flame
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how is 9*7=36

dense phoenix
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uhh

copper flame
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but yeah can you see the pattern here

dense phoenix
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u get my point

dense phoenix
copper flame
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yeah so just sum them up

dense phoenix
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oki

copper flame
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problem solved

dense phoenix
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thank u very much

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now time for rectangles

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i now need to find how many rectangles

copper flame
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greatttt

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you should try first

dense phoenix
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yes i will do so

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ok i got all the squares now im gonna start the rectangles

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ok so

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lets say a 1x2/2x1 rectangle

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its 9x8 + 7x10=142

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damn im so smart

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met a good teacher

copper flame
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that doesn't seem right

dense phoenix
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why not

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one sec lemme check avain

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again

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if i want to count all the 1x2 rectangles

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it means

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its 7x10=70

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and the 2x1 is 8x9=72

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isnt this correct

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general formula

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here it means nb of quadrilaterals of dimensions XxY

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it should be correct

copper flame
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I am doin my own hw rn 😭

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But you can send your answer here and I will check

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I would do it different way tho

dense phoenix
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okay

copper flame
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just finish my hw, here is an approach for ya

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consider choosing diagonal segments

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any rectangle consist of 2 diagonal lines

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so by bijection, the number of diagonal line is 2 times the number of rectangles