DAY 391

Which three consecutive, even numbers, when multiplied together, will give the product 8xxxx2 ? The x's represent four digits, though not necessarily the same ones.

Answer:


884,352


Since 90 cubed is 729,000 and the product of the three numbers  is over 800,000,  all three numbers must begin with 9.  Since they are even, the numbers must be either 90, 92, and 94, or 92, 94, and 96, or 94, 96, and 98. The product must end with 2. Looking at the second digits of 90, 92, and 94 - 0 x 2 x 4 = 0 - ending digit 0. Looking at the second digits of 92, 94, and 96 - 2 x 4 x 6 = 48 - ending digit 8. Looking at the second digits in 94, 96, and 98 ------- 4 x 6 x 8 = 192 - ending digit 2, which is what is required.  So 94 x 96 x 98 = 884,352.