The New Sudoku Players' Forum

[rjamil]

Which three digits number has certain peculiarity that it is a perfect square and when rotate 180°, then it is also a perfect square?

[Leren]

Withdrawn.

[StrmCkr]

square of 961 = 31
square of 169 = 13

whoms answer is also the reverse of the tops answer {180 rotation}

[rjamil]

We know that the only digits which can be rotated 180° and still be read as a digit are 0, 1, 6, 8 and 9. The digits, 0, 1 and 8 remain 0, 1 and 8, but 6 becomes 9 and 9 becomes 6. Therefore, the possible numbers
are 9, 16, 81, 100, 169 and 196, etc. Out of these, 196 is the only three digits number which becomes a perfect square of 14; and when rotated 180°, because 961 is the perfect square of 31. Hence, 196 is the number.

[rjamil]

Another point of view is that, if three digits perfect square 196 flipped upside-down instead of rotating 180° (i.e., digits will not change the places) then it becomes 169, which is also a three digits perfect square.

[StrmCkr]

square of 961 = 31
square of 169 = 13

whoms answer is also the reverse of the tops answer {180 rotation}

Out of these, 196 is the only three digits number which becomes a perfect square of 14

??? the square root of 169 = 13... how is that not a perfect square?

to further your comments that followed, i did a horizontal mirror = 180 degree rotation. { orientation changes } last is first, first is last.

and when rotate 180°

ie 1 type of rotation...


if you do a vertical mirror {a different type of 180 degree rotation} the number can swap from 6-9 etc
169 = 196
which both have perfect squares.
13 and 14 respectfully.

now if u do a vertical mirror and horizontal mirror you can swap the number and change order.
169 = 196
| |
691 = 961

which is 2 sets of 180 degree rotation . and only the 196 = 961 has perfect squares.

[rjamil]

Actually, all three answers are correct provided that the three digits number is rotated in three different directions.

169 <=> 961 (rotate digit positions 180° on x axis but not mirror image left-side right);
169 <=> 196 (either rotate 180° on y axis or mirror image up-side down); and
196 <=> 961 (either rotate 180° clock wise or counter clock wise).

Hint: write three digits number on transparent sheet and then try to rotate the sheet various way.

[StrmCkr]

Code: Select all

Hint: write three digits number on transparent sheet and then try to rotate the sheet various way.

i used an actual mirror