Hey guys!
I have a grid - in math question that I forgot how to do. I know there’s a certain way to do it without having to go through every single possibility.
Here’s the question:
What is the greatest four-digit integer that meets the following three restrictions?
- All of the digits are different.
- The greatest digit is the sum of the other digits.
- The product of the four digits is divisible by 10 and not equal to zero.
Does anyone know an efficient way to do this grid-in?
Thanks in advance and feel free to post any other math questions you may have!
There is a consolidated “SAT Math Questions” thread under the sub-topic “SAT Preparation.”
For your question, it is a good idea to pick the digits first. The product of the digits is a positive multiple of 10, so we have the following conditions:
- The # contains 5
- The # contains an even nonzero digit, and the # does not contain 0
Greedily assign 9 as the largest digit. The remaining digits must be 40 or 31 or 22 (since 9 = 5 + two other digits). 40 doesn’t work since 0 cannot be a digit, 22 doesn’t work since the digits are distinct, and 31 doesn’t work since the product of the digits is divisible by 10.
Next try 8 as the largest digit. Now the remaining two digits are 30 or 21. Again, 30 doesn’t work but 21 does.
The best case scenario uses the digits 8, 5, 2, 1 and 8521 is the largest such number.
Thanks! I’ll make sure to post on that thread next time