Math Project :|

Puzzle 1
What four digit number has digit 2 smaller than digit 4 which is two thirds of digit 1 which is two thirds of digit 3 which is three times digit 2?

Answer: 6394.
Working backwards:
Digit3 can only be 3, 6 or 9 (as it's 3 x Digit2).
Digit2 can only be 1, 2 or 3.
Digit1 can only be 2, 4 or 6.
But, since Digit4 is two thirds of Digit1, Digit1 must be 6. Making Digit4 4 and making Digit3 9. Making Digit2 3.
Giving 6394. QED.

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Puzzle 2
If you were to spell out the numbers in full, (One, Two, Three, etc), how far would you have to go until you found the letter 'A'?

Answer: 1000.
One thousAnd.
Unless you use British English when the answer becomes 101 = one hundred And one.

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Puzzle 3
As my birthday approaches I start to collect leaves - a little bizarre perhaps, but I enjoy it!
On the first day of the month I collect 1 leaf, on the second day I collect 2 leaves, the third day I collect 3 leaves, and so on.
By my birthday I will have collected 276 leaves altogether. On which day of the month is my birthday?

Answer: On the 23rd.
276 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23.

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Puzzle 4
Take the number of days in a leap year, add the number of months with 30 days, divide by the number of loaves in a baker's dozen, add the number of days in March, add the square root of nine, divide by the number of days in a week.
Which month are you left with?

Answer: September.
The numbers used are 366, +11, /13, +31, +3, /7 = 9.

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Puzzle 5
How quickly can you find the answer to:
5  x  4  x  3  x  ...  x  -3  x  -4  x  -5

Answer: Zero.

In full the question is:
5  x  4  x  3  x  2  x  1  x  0  x  -1  x  -  2  x  -3  x  -4  x  -5
As you can see, there is a x 0 in there, and anything times zero is zero.

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Puzzle 6
Are there more square inches in a piece of carpet 15 yards by 5 yards or feet in a 20 mile walk?

Answer: Feet in a 20 mile walk.
There are 12 inches in a foot, and 1,760 yards in a mile.
There are 105,600 feet in a 20 mile walk but only 97,200 square inches in a piece of carpet 15 yards by 5 yards.

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Puzzle 7
I have three daughters and each has one brother. How many children do I have?

Answer: 4.
I have three girls and one boy.
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Puzzle 8
Fred can eat 27 chocolates in a hour, Alice can eat 2 chocolates in 10 minutes, and Kelly can eat 7 chocolates in 20 minutes.
How long will it take them to share and eat a large box of 120 chocolates whilst watching a movie?

Answer: 2 hours.
In one hour, Fred eats 27 chocolates, Alice eats 12, and Kelly eats 21. A total of 60 chocolates. Therefore 120 chocolates would take 120 ÷ 60 = 2 hours. QED.
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Puzzle 9
Using eight eights and addition only, can you make 1000?

Answer: 888 + 88 + 8 + 8 + 8 = 1000.
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Puzzle 10

What is the smallest integer, which, when multiplied by 2 gives a number consisting of only 8's?

Answer: 4
Since 4 x 2 = 8, and it's the smallest possible answer.