Named products
Can you find the solution to this equation? Each of the different letters stands for a different number.
Age
11 to 14
Challenge level
Problem
In this equation, each letter stands for a different digit:$$\frac{E\times I\times G\times H\times T } {F\times O\times U\times R }= T\times W\times O$$
What is the value of the product $T\times H\times R\times E\times E$ ?
Student Solutions
Answer: $0$
$$\frac{E\times I\times G\times H\times T } {F\times O\times U\times R }= T\times W\times O$$
letters used: $E, I, G, H, T, F, O, U, R, W$ total 10 letters
So digit $0$ must be used
$\therefore \dfrac{E\times I\times G\times H\times T } {F\times O\times U\times R }= T\times W\times O = 0$
$T$ appears on both sides so $T=0$
Hence the product $T\times H\times R \times E \times E =0$.