source string | problem string | solution string | messages list |
|---|---|---|---|
aops_forum | **p1.** Show that for every $n \ge 6$ , a square in the plane may be divided into $n$ smaller squares, not necessarily all of the same size.**p2.** Let $n$ be the $4018$ -digit number $111... 11222...2225$ , where there are $2008$ ones and $2009$ twos. Prove that $n$ is a perfect square. (Giving the square... | 1. **Problem 1:**
We need to show that for every \( n \geq 6 \), a square in the plane may be divided into \( n \) smaller squares, not necessarily all of the same size.
**Step 1:** Consider the case when \( n = 6 \). We can divide a square into 6 smaller squares by first dividing it into 4 equal smaller squares... | [
{
"content": "**p1.** Show that for every $n \\ge 6$ , a square in the plane may be divided into $n$ smaller squares, not necessarily all of the same size.**p2.** Let $n$ be the $4018$ -digit number $111... 11222...2225$ , where there are $2008$ ones and $2009$ twos. Prove that $n$ is a perfect squ... |
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