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This equation means that 25 to the 3/2 power equals x.  25 to the 3/2 power is (25 to the 1/2 power) raised to the 3rd power...or said another way, the (square root of 25) cubed.  The square root of 25 is 5 and 5 cubed is 125.

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Sometimes even with hard work, we just hit a dead-end when trying to solve a problem. Our best waking efforts just sometimes don't work. It makes sense to develop our intuition, even with regard to mathematics. Here is a puzzle that will help you gain confidence in your own intuition. What word is this: hijklmno ? It is very common; I’m sure you use it every day. Try hard for maybe... read more

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The Mutilated Chessboard A chessboard has 64 squares, 8 by 8. If you have 32 dominoes, each the size of 2 side-by-side chessboard squares, you’ll be able to exactly cover the chessboard with the dominoes. (In fact, there are very many ways you could arrange the dominoes to cover the 64 squares of the board!) But suppose you cut off any two diagonally opposite corner squares of the... read more

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How Was This Possible? I hiked the Grand Canyon earlier this year, as I've done for many years. I started down the trail at exactly 7 am, and hiked at an irregular pace, slowing and stopping occasionally to enjoy the views. I’m not sure what time I got to the river, but I got there before dark and spent the night camped at the river. I started back up the same trail at exactly 7 am... read more

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What Did I Buy? I went to the hardware store the other day to buy a common item that I needed for my home. I bought just 1 for a dollar, but I noticed that I could have bought 10 for $2, 100 for $3, or even 1000 for $4. What did I buy? This puzzle is another exercise in problem solving techniques. The math is not hard, but finding a solution requires some creative thinking and careful... read more

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The World-Wide Highway Sometimes, intuition helps us solve problems, but sometimes not. When intuition fails, math can help. What is your intuition about the following puzzle? If we could build a road in a circle around the world at the equator, it would be about 25,000 miles long. To raise this road 5 feet above the surface, all the way around, how much longer would the road need... read more

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The Four Ones Problem Use the digit "1" exactly 4 times, no other numbers, and any number of standard symbols from arithmetic or algebra to make a formula that equals 5. (There may be more than one formula that works.) For example: 0 = 1 – 1 + 1 - 1 1 = 1 * 1 * 1 * 1 2 = (1 + 1) / 1 / 1 Extra Credit: What is the SMALLEST whole number that CANNOT... read more