# 6MMM^3

The 6th Monday Math Madness is online now. This week is actually not so hard, even though there are two different problems… I was able to get both of the answers in about 30 minutes (assuming I didn’t make any huge errors). I especially like the first question, because it can be easily transposed into a slightly more difficult and fun problem…

The first question reads:

• Start with 500 gallons of mayonaise.
1) Mix in 10 gallons of ketchup. Stir until completely mixed.
2) Remove 10 gallons of the mixture.
3) Repeat steps 1 and 2 until the mixture is approximately 50% mayonaise and 50% ketchup.How many iterations will it take to do this?

Here’s the slightly modified problem:

• Start with 500 gallons of mayonaise.
1) Mix in 3 gallons of mayonaise and 7 gallons of ketchup. Stir until completely mixed.
2) Remove 10 gallons of the mixture.
3) Repeat steps 1 and 2 until the mixture is approximately 40% mayonaise and 60% ketchup.How many iterations will it take to do this?Â

That slight change makes it more difficult! But fun fun fun!

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## 3 comments

1. surely the first problem doesn’t reach 50/50, it just gets infinitely close.. i guess if you were to round it than you would reach it.
I thought I got the answers but deadline passed anyways.