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Jane wrote a number on the whiteboard. Then, she looked at it and she noticed it lacks her favourite digit: 5. So she wrote 5 at the end of it. She then realized the new number is larger than the original one by exactly 1661. What is the number written on the board?

Replace letters with digits to maximize the expression: \[NO + MORE + MATH\] (same letters stand for identical digits and different letters stand for different digits.)

Which triangle has the largest area? The dots form a regular grid.

What is the ratio between the red and blue area? All shapes are semicircles.

In a parallelogram \(ABCD\), point \(E\) belongs to the side \(CD\) and point \(F\) belongs to the side \(BC\). Show that the total red area is the same as the total blue area:

The figure below is a regular pentagram. What is larger, the black area or the blue area?

A circle was inscribed in a square, and another square was inscribed in the circle. Which area is larger, the blue or the orange one?

In a square, the midpoints of its sides were marked and some segments were drawn. There is another square formed in the centre. Find its area, if the side of the square has length \(10\).

In a parallelogram \(ABCD\), point \(E\) belongs to the side \(AB\), point \(F\) belongs to the side \(CD\) and point \(G\) belongs to the side \(AD\). What is more, the marked red segments \(AE\) and \(CF\) have equal lengths. Prove that the total grey area is equal to the total black area.

Replace the letters with digits in a way that makes the following sum as big as possible: \[SEND +MORE +MONEY.\]