Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the equation true.
Hint
What multiplication has to happen to be left with a single digit in the result?
What will happen to the power of 10 in the result?
What will happen to the power of 10 in the result?
Answer
There are multiple solutions. Possible answers are:
5 x 10^4 x 2 x 10^3 = 1 x 10^8
5 x 10^1 x 6 x 10^7 = 3 x 10^9
5 x 10^2 x 8 x 10^3 = 4 x 10^6
Source: Luke Cole
This isn’t the best hint: “What multiplication has to happen to be left with a single digit in the result?” because it implies that the two bases on the left have to multiply to a single digit. Like 2*3=6.
There are two types of solutions: A) ones where the base digits on the left multiply to a single base digit on the right, and the two exponents on the left add to the exponent on the right… OR
B) Ones where the base digits on the left multiply to a double-digit base digit on the right THAT ENDS IN ZERO (which can only happen with 5*even#), and the two exponents on the left add to ONE LESS THAN the exponent on the right, which becomes 1 bigger due to the zero in the product.
The hint is suggesting only solutions of type A, but the answers provided are all solutions of type B.