Pick a 3 digit number.
Divide the number by 6. Write down the remainder.
Divide the number by 7. Write down the remainder.
Divide the number by 8. Write down the remainder.
Add the three remainders together.
What starting number should you pick to get the greatest possible sum?
#iTeachMath
Divide the number by 6. Write down the remainder.
Divide the number by 7. Write down the remainder.
Divide the number by 8. Write down the remainder.
Add the three remainders together.
What starting number should you pick to get the greatest possible sum?
#iTeachMath
Comments
I randomly tried 983 and got a sum of remainders of 15.
Then I tried both solutions mentioned, and they are quick and clever.
How about extending the problem to ask for the range of values - what's the smallest, what's the biggest, and then what patterns might we find?
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The elegance of that solution seemed to me that 335 must be the smallest number where we can max out the remainders. But 167 works similarly well.