# TRICKS FOR ARITHMATIC

## Added on: 13th Dec 2015

**THE MAGIC STRING**

**Imagine that you tied a string around the equator of the Earth so tight**

** that you couldn’t even fit a razor blade underneath. Now let’s**

** imagine that we lengthen the string by only 1 metre. Of course we would**

** now have some slack around the equator, but how much? It’s hard to **

**believe but the answer is that the string would now clear the Earth by **

**16cm all the way around! If you want a party trick just google the proof. **

**It will fit onto a napkin.**

**THE COIN SORTER**

**Lay out a bunch of coins on the table and tell your friend to blindfold you. **

**Ask him how many of the coins are facing heads up. Whatever number**

** he tells you, flip that many coins over (any coins) and move them to a **

**separate pile. You will now have two piles with the same number of **

**heads and tails and your friend will think you are a wizard after he counts **

**them! To add some drama, pretend to select the coins you flip carefully. **

**Why does this work? It’s maths!**

**FIGURE OUT THE LAST NUMBER OF ANY BARCODE**

**The last digit in any barcode (the one that is apart from the rest and **

**not under the bars) is actually used by the computer to check and **

**make sure it reads the numbers right. Impress your friends by being **

**able to “guess” these! Starting from the right add every odd digit three**

** times and every even digit once. Then subtract the last digit of the**

** total from 10. Here is an example:**

**For 03600029145 you should calculate something like this:**

**5+4+1+9+2+0+0+0+6+3+0+**

**5+1+2+0+6+0+**

**5+1+2+0+6+0 = 58**

**10 – 8 = 2**

**The extra digit would be 2!**

**CHECK ANY MULTIPLICATION PROBLEM**

**This makes use of a trick called digital roots. For 2878 x 4902 = 14107956 **

**just do the following:**

**Find the digital roots of the first number:**

**2+8+7+8 = 25**

**2+5 = 7**

**Do the same for the second and third numbers. **

**We’ll spare you the time and tell you that they are both 6. **

**So, take 7×6 (the digital roots of the two numbers you are multiplying) **

**which equals 42. 4+2 = 6. Since 6 = 6 the math is right!**

**THE CALENDAR TRICK**

**Tell your friend to select a square of 9 numbers on any calendar. **

**For example:**

**14 15 16**

**21 22 23**

**28 29 30**

**No matter what square he chooses you can quickly tell him what **

**they all add up to. Just multiply the middle number by 9! 22 x 9 = 198**

**THE CALENDAR TRICK ON STEROIDS**

**This time tell your friend to select a 5×4 box around any 20 numbers**

** on the calendar. All you have to do to figure out what they all add up to**

** is take the lowest number and highest number and add them together. **

**Then multiply the answer by 10.**

**CALENDAR TRICK EXTENDED**

**The previous two tricks will actually work on any grid of numbers **

**as long as it is continuous!**

**THE MONTY HALL PROBLEM**

**First gaining public attention when it was sent to Ask Marylin **

**(Marlylin vos Savant’s column in Parade Magazine), the answer to this **

**statistical anomaly at first caused quite an uproar. Some Phd’s and **

**mathematicians (even from MIT!) wrote to the magazine in disbelief. **

**After several months though, with some scientists even designing **

**computer simulations to prove it, the answer to the Monty Hall Problem **

**showed itself to be correct. And here is the problem as it was written to **

**Marylin in 1990: Suppose you’re on a game show, and you’re given the **

**choice of three doors: Behind one door is a car; behind the others, goats.**

** You pick a door, say No. 1, and the host, who knows what’s behind the **

**doors, opens another door, say No. 3, which has a goat. **

**He then says to you, “Do you want to pick door No. 2?” **

**Is it to your advantage to switch your choice?**

**The answer is incredibly that yes, your chances increase if you switch doors. **

**You’ll have to google it to find all the proofs but a quick way to visualize it **

**is to imagine not 3 doors but 1 million doors. You choose 1 door and then **

**the game show host opens all but 1 other door. This time the answer **

**becomes more obvious. You should definitely switch. **

**Would you really trust yourself to have picked the right door out **

**of 1 million? Here is another intuitive explanation offered by Matthew Carlton:**

**An intuitive explanation is that if the contestant picks a goat **

**(2 of 3 doors) the contestant will win the car by switching as the other **

**goat can no longer be picked, while if the contestant picks the car **

**(1 of 3 doors) the contestant will not win the car by switching.**

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