Squirrels

The squirrels discovered a bush with hazelnuts. The first squirrel plucked one nut, the second squirrel two nuts, and the third squirrel three nuts. Each new squirrel always tore one nut more than the previous squirrel. When they plucked all the nuts from the bush, they divided them so that each squirrel received six nuts. How many squirrels tore nuts?

Final Answer:

n =  11

Step-by-step explanation:

$$\begin{gathered} v_1=1 \\ {v}_2=2 \\ {v}_3=3 \\ d=v_2-v_1=2-1=1 \\ v(n)=v_1+(n-1)\cdot d=1+n-1=n \\ 6\cdot n=v_1+v_2+v_3+\dots +v_n \\ 6\cdot n=1+2+3+\dots +n \\ 6\cdot n=(1+n)+(2+n-1)+(3+n-2)+\dots \\ 6\cdot n=(1+n)+(n+1)+(n+1)+\dots \\ 6\cdot n=n/2\cdot (1+n) \\ 6=1/2\cdot (1+n) \\ n=11 \\ \text{ Verifying Solution: } \\ {s}_1=6\cdot n=6\cdot 11=66 \\ {s}_2=1+2+3+4+5+6+7+8+9+10+11=66 \end{gathered}$$

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