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# 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?

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?

```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 1/4x+(1/4*1/4)x+1/2x+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 5w+3=x. When four people deal, say each get z number of cards, then 4z+7=x and when three people deal, say each get y number of cards, then 3y+7=x. Solving 4z+7=3y+7 gives 4z=3y. 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 5w+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.