#Math behind solving a lights out puzzle how to#
#Math behind solving a lights out puzzle full#

Pour the two gallons of water in the 5-gallon jug into the 3-gallon jug, Then, pour all of the water from the 3-gallon jug back into the 8-gallon jug.

#Math behind solving a lights out puzzle full#

Pour water from the 5-gallon jug into the 3-gallon jug until it is completely full (leaving 2 gallons in the 5-gallon jug). Start by completely filling up the 5-gallon jug with water. A coin total of 7 is a solid contender because it shows up on almost every list…except for the groups of 5, so the answer must be a different number.Īt this point, you’ll notice that there isn’t a number that appears on every list, so you’ll have to start extending them as follows until you find the answer:ġ90 handshakes (19+18+17+16+.+3+2+1=190) Now that you have a list of coin total possibilities for each statement, you have to the identify the lowest number that is present on every list. Possible Coin Totals for Groups of 6: 7, 13, 19, 25, 31, 37,…įinally, make a list of possibilities for the last statement: but when she arranges the coins in groups of seven, there are no coins left over.

Possible Coin Totals for Groups of 3: 4, 7, 10, 13, 16, 19,… You can then go ahead and repeat this process for the statement when she arranges the coins in groups of three, five, or six, there is also just one single coin left over. Let’s assume that this is the only true statement that we know, then we could conclude that her total number of coins must be one more than a number that is divisible by two. In this case, let’s go ahead and create a chart that models all of the possible scenarios, starting with the fact that when she arranges the coins in groups of two, there is one single coin left over.

#Math behind solving a lights out puzzle how to#

This is a very challenging problem to solve mentally, so using a pen and paper will be a big help (if you are a hands-on learner, you can use real coins to support your thinking and model how to solve this riddle). What is the fewest amount of coins she could have? But when she arranges the coins in groups of seven, there are no coins left over. When she arranges the coins in groups of three, five, or six, there is also just one single coin left over. When she arranges the coins in groups of two, there is one single coin left over. You can choose to skip this practice problem if you would like. In case you are feeling a bit rusty and need a quick refresher on how to go about solving math riddles, below is a bonus practice problem that is worked out step-by-step. You’ll be surprised by how the problem will become more manageable when you return.

If you are stuck on a problem, take a short break, and do something else like taking a short walk. Whenever you find a solution, ask yourself “does my answer make sense?” Utilize strategies such as visualizing, drawing diagrams, and trial-and-error when you don’t know where to start.ĭon’t get discouraged! When you are struggling and making mistakes, you are in the process of learning. Read each math riddle carefully and think about the problem for a while before doing anything. Helpful Advice Before You Begin…īefore you start working on solving all 10 riddles, here are a few helpful hints for overcoming the inevitable moments when you get stuck and/or are considering giving up on trying to solve the problem: It is recommended that have a pen, paper, and a calculator on-hand when attempting to solve any of these riddles, as drawing a diagram and working out the math by hand can be extremely helpful. Today’s post shares 10 super fun math riddles for ages 18+ that were created to challenge the adult mind and they are appropriate for individuals ages 16 and up.Įach math riddle is a unique opportunity to apply your problem-solving skills, mathematical thinking, arithmetic, reasoning, and logic. Working on math riddles as an adult is a great way to keep your mathematical reasoning and problem-solving skills sharp while having a lot of fun at the same time.