7.4. There are 20 sticks of lengths $1, 2, \ldots, 20$. Can they be used to form a) a square; b) an equilateral triangle? (All sticks must be used without breaking them.)
Answer: a) impossible; b) possible. Solution. a) The sum of the lengths of all 20 sticks is 210. This number is not divisible by 4, and therefore it is impossible to form a square. b) It is possible to distribute 210 into three equal parts of 70 each in different ways, for example, as follows: $(20+19+18+13)+(17+16+15+14+8)+(1+2+3+4+5+6+7+9+10+11+12)$.