For Four 4's ("Student Calculator Math Book", 1980)

An exercise from the Student Calculator Maths Book, published by Texas Instruments in 1980:

Can you build all the whole numbers from 1 to 100 using only four 4's? Use only the $+$, $-$, $\times$, $\div$, $($, $)$, $.$, $x!$, $x^2$, $=$ and 4 keys on your calculator. All the whole numbers up to 119 have been built with just four 4's - how many can you find?
$1=\frac{44}{44}$
$2=\frac{4}{4}+\frac{4}{4}$
$3=(4+4+4)/4$
$4=(4!-4-4)/4$
$5=\frac{4\times 4 + 4}{4}$
$6=4+\frac{4+4}{4}$
$7=4+4-\frac{4}{4}$
$8=4-4+4+4$

Note the rule that you have to use all four of the 4's for each number (which makes it more challenging).

Additional note: David Wheeler has compiled a catalogue of 'Four fours' solutions for integers up to 40,000 (it depends on what you will allow as arithmetical operations).

('Read more' for my answers)

Number Maths expression Calculator key presses
9 $9=4+4+\frac{4}{4}$
4 + 4 + 4 / 4
10 $10=4-4+\frac{4}{.4}$
4 - 4 + 4 / . 4
11 $11=4^2 - 4 - \frac{4}{4}$
4 x^2 - 4 - 4 / 4
12 $12=4^2 - 4 + 4 -4$
4 x^2 - 4 + 4 - 4
13 $13=4^2 - 4 + \frac{4}{4}$
4 x^2 - 4 + 4 / 4
14 $14=4^2-\frac{4+4}{4}$
4 x^2 - ( 4 + 4 ) / 4
15 $15=4\times 4 - \frac{4}{4}$
4 x 4 - 4 / 4
16 $16=\frac{4}{.4}+\frac{4!}{4}$ or $4\times 4 + 4 - 4$
4 / . 4 + 4 ! / 4
17 $17=4\times 4 + \frac{4}{4}$
4 x 4 + 4 / 4
18 $18=\frac{4}{.4}+4+4$
4 / . 4 + 4 + 4
19 $19=4! - 4 - \frac{4}{4}$
4 ! - 4 - 4 / 4
20 $20=4! - 4 + 4 - 4$
4 ! - 4 + 4 - 4

 

Number Maths expression Calculator key presses
21 $21=4! - 4 + \frac{4}{4}$
4 ! - 4 - 4 / 4
22 $22=4! - \frac{4+4}{4}$
4 ! - ( 4 + 4 ) / 4
23  
 
24 $24=4! + \frac{4-4}{4}$
4 ! + ( 4 - 4 ) / 4 
25  
 
26 $26=4! + \frac{4+4}{4}$
4 ! + ( 4 + 4 ) / 4
27 $27=4! + 4 - \frac{4}{4}$
4 ! + 4 - 4 / 4
28 $28=4! + 4 + 4 - 4$
4 ! + 4 + 4 - 4
29 $27=4! + 4 + \frac{4}{4}$
4 ! + 4 + 4 / 4
30 $30= \frac{4+4+4}{.4}$
( 4 + 4 + 4 ) / . 4

 

 

Number Maths expression Calculator key presses
31 $31=4^2 + 4^2 - \frac{4}{4}$
4 x^2 + 4 x^2 - 4 / 4
32 $32=4^2 + 4^2 + 4 - 4$
4 x^2 + 4 x^2 + 4 - 4
33 $33=4^2 + 4^2 + \frac{4}{4}$
4 x^2 + 4 x^2 - 4 / 4
34 $34=44 - \frac{4}{.4}$
4 4 - 4 / . 4
35 $35 = 4! + \frac{4.4}{.4}$
4 ! + 4 . 4 / . 4
36 $36 = (4+\frac{4+4}{4})^2$
(4 + ( 4 + 4 ) / 4 ) x^2

(Work in progress...)

Add new comment

Please answer the question