Question

A square of nine number is marked in calendar the sum of these numbers is 90. What are the numbers

Answer 1

AnswEr :

• The required numbers are 2, 3, 4, 9,10, 11, 16,17and 18.

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GivEn :

• The numbers marked in the calendar are square in the arrangement.

• Sum of the numbers is 90.

SoluTion :

Since it is square with 9 numbers, 3 numbers would be it's breadth and other 3 would be length !!

Let us assume that the smallest number be x.

Then, the numbers will be,

• x

• x + 1

• x + 2

For next week (same day),

• x + 7

• x + 8

• x + 9

Next week (same day)

• x + 14

• x + 15

• x + 16

Sum of these numbers is 90 (Given)

➝ x + (x + 1) + (x + 3) + (x + 7) + (x + 8) + (x + 9) + (x + 14) + (x + 15) + (x + 16) + (x + 17) = 90

➝ 9x + 72 = 90

➝ 9x = 90 - 72

➝ 9x = 18

➝ x = 18/9

➝ x = 2

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So, the numbers are :

➠ x = 2

➠ x + 1= 2 + 1 = 3

➠ x + 2 = 2 + 2 = 4

➠ x + 7 = 2 + 7 = 9

➠ x + 8 = 2 + 8 = 10

➠ x + 9 = 2 + 9 = 11

➠ x + 14 = 2 + 14 = 16

➠ x + 15 = 2 + 15 = 17

➠ x + 16 = 2 + 16 = 18

$\therefore$ The required numbers are 2, 3, 4, 9,10, 11, 16,17 and 18.

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