Problem 3. Senya cannot write some letters and always makes mistakes in them. In the word TETRAHEDRON he would make five mistakes, in the word DODECAHEDRON - six, and in the word ICOSAHEDRON - seven. How many mistakes would he make in the word OCTAHEDRON?

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# Answer. 5.

Solution. If Senya mistakenly writes D, then out of the letters O, E, K, A, E, R, which are also in DODEKAEDR, he makes three mistakes and writes three correctly. But all these letters, except E, are also in IKOSAEDR, which means he will write at least two letters correctly and cannot make 7 mistakes. Therefore, Senya writes the letter D correctly. Then he inevitably makes mistakes in writing all the other letters in the words DODEKAEDR and IKOSAEDR, and in the word TETRAEDR, he writes the letter D correctly and also writes the letter T correctly, but makes mistakes in all the others. Now it is clear that in the word OKTAEDR, Senya will make five mistakes.