Number Pattern

Directions: Using the digits 1 to 7, at most one time each, place a digit in each circle so that the sum of the numbers in 3 squares (the middle horizontal line or 2 diagonals) are same.

e.g A+B+C or D+B+E or F+B+G

Is there more than one solution?

Hint

Be strategic to think about the number in the center circle.

Answer

A possible answer

5 2
7 4 1
6 3

Source: Al Oz

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11 comments

  1. a=7 b=1 c=2
    d=6 e=3
    f=5 g=4

  2. A=2 B=7 C=5
    D=3. E=4
    F=1. G=6

    or change the pairing to get similar solutions

  3. hi c if ur reading dis

  4. :]
    also i got dat answer off d answer box thingy soz i CANNOT understand this 😅

  5. C ru there if UR then pleez rspond

  6. Rudolf Österreicher

    I don’t understand the directions. There are no circles in the image provided, but I guess the squares are the circles. But then the directions also mention squares. It says the sum of three squares should be the same – but the same as what? Each square contains only a single-digit-number, which are all different, so no 3 squares have the same “sum”.
    Do you mean that the sums along the three lines ABC, FBG and DBE should be the same? In your example, the sum along ABC = the sum along DBE = the sum along FBG = 12.
    In that case:

    The possible sums of three different numbers from 1 to 7 are:
    1+2+3=6
    1+2+4=7
    1+2+5=1+3+4=8
    1+2+6=1+3+5=2+3+4=9
    1+2+7=1+3+6=1+4+5=2+3+5=10
    1+3+7=1+4+6=2+3+6=2+4+5=11
    1+4+7=1+5+6=2+3+7=2+4+6=3+4+5=12
    2+4+7=2+5+6=3+4+6=13
    1+6+7=2+5+7=3+4+7=3+5+6=14
    2+6+7=3+5+7=4+5+6=15
    3+6+7=4+5+7=16
    4+6+7=17
    5+6+7=18

    Only the sums 10, 12 and 14 have three sums where one of the numbers appears 3 times:
    The sums 1+4+7=2+4+6=3+4+5=12 all have the number 4 and contain all natural numbers from 1 to 7.
    The sums 1+2+7=1+3+6=1+4+5=10 all have the number 1 and contain all natural numbers from 1 to 7.
    The sums 1+6+7=2+5+7=3+4+7=14 all have the number 7 and contain all natural numbers from 1 to 7.

    So the only solutions other than the one provided by the author are
    ..2 4
    3 1 6
    ..5 7

    and

    ..1 2
    3 7 4
    ..5 6

    plus all the variants of these three solutions (8 each) where the endpoints of the lines ABC, BFG and/or DBE are swapped, for example
    ..6 2
    3 7 4
    ..5 1

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