# 6 Math riddles (Only for geniuses)

Try these riddles if you are a genius.

1. Lion A says to Lion B: "if I adopt a cub of yours I will have three times the number of cubs you have and if you adopt a cub of mine, then we will have the same number of cubs". How many cubs does each lion have?

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*2. *Sara and Mary are two sisters. Two years ago Sara was three times as old as Mary while in three years' time she will be two times Mary's age. How old are the sisters now?

*3. *Grandpa Mustafa has left quarter of his wealth to his daughter and quarter of what he left to his daughter to his granddaughter. He left half of his wealth to his wife and the remaining $2000 to an orphanage. How much was his total wealth?

*4. *Which number appears the most number of times between and including 1 and 1000?

*5.* Two pairs of twins* *Mr. X & Mr. Y, and Ms. W & Ms. Z live down the same lane. The house numbers of each pair are two digits and the reverse of each other. The difference between the two numbers ends with number 3. What are the 4 house house numbers?

6. Some number of cards are missing in a complete pack. When five people deal, three cards remain. When four people deal, seven remain and when three people deal, seven cards remain. How many cards are there?

ANSWERS

*Answer **1**:** Lion **A** has **5** cubs and Lion **B** has **3** cubs**.** *
*How**?** Say Lion **A** has x cubs and Lion **B** has y cubs**.** When Lion **A** adopts one it will have x**+**1** and Lion **B** will have y**-**1.** Hence**,** x**+**1**=**3**(**y**-**1**)**.** When Lion **B** adopts one it will have y**+**1** and Lion **A** will have x**-**1.** Hence**,** y**+**1**=**x**-**1**;** y**+**2**=**x**.** Substituting x**=**y**+**2** **in** x**+**1**=**3**(**y**-**1**)** gives y**=**3.** Then**,** x**=**3**+**2**=**5.** So**,** Lion **A** has **5** cubs and Lion **B** has **3** cubs**.** *

*Answer **2**:** Sara is **17** and Mary is **7.*
How? *Say Sara is x years and Mary is y years today**.** Two years ago sara was x**-**2** and Mary y**-**2.** **So** **(**x**-**2**)**=**3**(**y**-**2**)**.** In three year's time sara will be x**+**3** and Mary y**+**3.** So x**+**3**=**2**(**y**+**3**)**.** Solving the simultaneous equations gives x**=**17** and y**=**7.*

*Answer **3**:** Total wealth is $**16000.*
How? *Say total wealth is x**.** Then **1**/**4**x**+**(**1**/**4*****1**/**4**)**x**+**1**/**2**x**+**2000**=**x**.** Solving **this** gives x**=**16000.*

*Answer **4**:** **1** appears the most number **of** times**.*
How? *1** appears **301** times **as** we include **1** and **1000** **while** the other numbers appear only **300** times each **with** zero appearing the least number **of** times**.** *

*Answer **5**:** **29**,** **92** and **18**,** **81.*
How? *Write the digits **with** the last digit **of** numbers to **get** the difference **3.** **E**.**g**.** **9**-**6**,** **8**-**5**,** and don't forget **12**-**9** where you have **2** and **9** **as** the last digits and **11**-**8** where **1** and **8** are the last digits**.** Now test each number **with** the reverse **of** it**.** **96**-**69** **for** instance does not end up **in** **3.** The answer is **29**,** **92** and **18**,** **81.** *__(____See table below____)__

*Answer **6**:** **43** cards*
How? *Say total cards **in** the pack is x**.** When five people deal**,** say each **get** w number **of** cards**.** So **5**w**+**3**=**x**.** When four people deal**,** say each **get** z number **of** cards**,** then **4**z**+**7**=**x and when three people deal**,** say each **get** y number **of** cards**,** then **3**y**+**7**=**x**.** Solving **4**z**+**7**=**3**y**+**7** gives **4**z**=**3**y**.** The number is a multiple **of** **3** and **4** **with** **7** added to it**.** When **3** is deducted **from** **this** number**,** it should also be divisible by **5** to satisfy **5**w**+**3**=**x**.** Let's start **with** **12.** *
*12**+**7**-**3**=**16** is not divisible by **5*
*24**+**7**-**3**=**28** is not divisible by **5*
*36**+**7**-**3**=**40** is divisible by **5.** So it should be **36**+**7** **=** **43.** *

*Did you just nail it? Well! You are a genius then. See you again with another interesting topic.*