Number Puzzles

1.How can I get the answer 24 by only using the numbers 8,8,3,3.

You can use the main signs add, subtract multiply and divide.

The Solution . . .

We know of two solutions.

1) Supplied by "mathsyperson":

8/(3-(8/3))

= 8/(1/3)
= 24

2) Supplied by "puzzler09", using factorials:

((8 x 3!)/3)+8

= ((8 x 3 x 2 x 1)/3)+8
= (48/3)+8
= (16)+8
= 24

3) Supplied by "Mark":

{3!/(cube root of 8)}*8

2.What 5-digit number has the following features:

If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.

The Solution . . .

Using an easy equation:

3(100000 + x) = 10x+1

(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)

Solving this gives:

10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x= 299999/7 = 42857

The answer is 42857.

3.When asked about his birthday, a man said:

"The day before yesterday I was only 25 and next year I will turn 28."

This is true only one day in a year - when was he born?

The Solution . . .

He was born on December 31st and spoke about it on January 1st.

4.What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

(Caution: Trick)

The Solution . . .

A Decimal Point

5.9 works nicely

5.A popular mathematical passtime:

Use exactly four 4's to form every integer from 0 to 50, using only the operators +, -, x, /, () (brackets) x² (square), and ! (factorial).

Example: 0 = 44-44

The Solution . . .

0 = 44-44
1 = 44/44 or (4+4)/(4+4) or (4/4) / (4/4)
2 = 4/4+4/4
3 = (4+4+4)/4
4 = 4*(4-4)+4
5 = (4*4+4)/4
6 = 4*.4+4.4
7 = 44/4-4
8 = 4+4.4-.4
9 = 4/4+4+4
10 = 44/4.4
11 = 4/.4+4/4
12 = (44+4)/4
13 = 4!-44/4
14 = 4*(4-.4)-.4
15 = 44/4+4
16 = .4*(44-4)
17 = 4/4+4*4
18 = 44*.4+.4
19 = 4!-4-4/4
20 = 4*(4/4+4)
21 = (4.4+4)/.4
22 = 44*sqrt(4)/4
23 = (4*4!-4)/4
24 = 4*4+4+4
25 = (4*4!+4)/4
26 = 4/.4+4*4
27 = 4-4/4+4!
28 = 44-4*4
29 = 4/.4/.4+4
30 = (4+4+4)/.4
31 = (4!+4)/4+4!
32 = 4*4+4*4
33 = (4-.4)/.4+4!
34 = 44-4/.4
35 = 44/4+4!
36 = 44-4-4
37 = (sqrt(4)+4!)/sqrt(4)+4!
38 = 44-4!/4
39 = (4*4-.4)/.4
40 = 44-sqrt(4*4)
41 = (sqrt(4)+4!)/.4-4!
42 = sqrt(4)+44-4
43 = 44-4/4
44 = 44.4-.4
45 = 4/4+44
46 = 44-sqrt(4)+4
47 = 4!+4!-4/4
48 = 4*(4+4+4)
49 = (4!-4.4)/.4
50 = 4!/4+44

(Note: people have managed to do this for 1000s of numbers!)