Solid math (hard)
I saw this in tweet today from Scientific American (link omitted intentionally). This is elegant and simple math puzzle that requires high math skills. User three numela 4′s and any math operations to produce number 55. It’s solvable without any tricks.
Pencil
Take a pencil, a ruler or any similar object and place it on top of point fingers. Now slowly start moving fingers closer together. One finger will start sliding but then it will stop and another finger will begin to slide and will also stop trading sliding action back to first finger. It doesn’t matter which finger will start sliding first but they will slide and stop in turns. Why ? There is perfectly good and simple explnation to this behavior.
Which finger is first to slide determined by which finger has lower friction resistance which in turn determined by weight of the object (we ignore case where object has different surface friction on each side which most pencils don’t). Usually finger farthest from center mass will start sliding first because it bears less weight and therefore less friction. As it approaches center the weight applied will increase hence friction will also increase and eventually it will be higher then friction of the stationary finger at which point moving finger will stop and another will start to slide. The whole process repeats.
Note, that friction of the moving object is less then friction of the stationary one with rest of things been equal. Hence sliding finger will have to move closer to the center to gain enough friction so it can trade sliding with the stationary finger.
Two boats
Two boats are approaching the pier. Person in each boat is pulling himself and boat in. One boat has another end of the rope tied to the pier where second boat has third person on pier pulling on another end of it’s the rope (see picture). All three people apply the same force – they all are pulling in rope equally. Which boat will reach peir fist ?
Similarly to the previous question the force applied to boat with two people on a rope is exactly the same as force applied to boat with only one person on a rope. In other words both boats will reach pier at the same time.
Two horses
Two horses pull ropes attaches to scales in opposite direction with the same stady force of 100 kg each. What weight do scales show?
Many would answer 100 + 100 = 200 which is completely wrong, they ignore third Newton’s law. The righ answer is the same 100 kg. Think about it, there is only one way to have rope tension be 100 kg – it’s to pull it from each end with force at 100 kg.
Simple math problems
Here are few simple math problems, you should be able to solve them quickly however they may be puzzling for kids. Write an equation with five 2s using only addition (+) operation to result in 28. Similarly, write an eqation using eight 8s that results in 1000, again only addition operation is allowed. And finaly write eqation that uses five 1s and results in 100, but here any simple opearion is allowed.
22+2+2+2=28, 888+88+8+8+8=1000, 111-11=100