Weekly Problem 42

7136 /www/nrich/html/content/id/7136/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> In the equation $\frac{E\times I\times G\times H\times T } {F\times O\times U\times R }= T\times W\times O$ . The same letter stands for the same digit and different letters stand for different digits. What is the value of the product $T\times H\times R\times E\times E$? If you liked this problem, <a href="http://nrich.maths.org/756&part=">here is an NRICH task</a> which challenges you to use similar mathematical ideas. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> If we rewrite the equation we get the product $E\times I\times G \times H\times T = T\times W \times O\times F\times O \times U \times R$. There are $10$ different letters here, so each number from $0$ to $9$ must be represented by one of the letters. So one letter is $0$. Any product where this letter appears is $0$. Hence both sides must include this letter. The only letter on both sides is $T$. Hence $T=0$ and the product $T\times H\times R \times E \times E =0$. </mdoxml> 2 3 0 0 1 0 0 Weekly Problem 42 - 2010 Weekly Problem 42 - 2010 Algebra Algebra - generally Algebra Using symbols Using, Applying and Reasoning about Mathematics Selecting and using information