Before I retired, I would give my students the following challenge:
Write expressions for all the numbers from 1 to 100 using only the digits in the current year in order and using the operations +, -, x, ÷ (or / for divided by), ^ (raised to a power), sqrt (square root), ! (factorial), and int (or [] for greatest integer function), along with grouping symbols.

So, the first problem of the new year is to use only the digits 2, 0, 2, 4, (and in that order) along with the operations listed above to write expressions for all the numbers from 1 to 24.

Extra credit for those who can go past 24 (consecutively).

Click here for a worksheet

Click here for solutions to previous years
Some Solutions to the Problem:

1 = 2 + 0! + 2 - 4
2 = 2 + 0 * 24
3 = 2 - 0! - 2 + 4
4 = 2 + 0 - 2 + 4
5 = -2 + 0! + 2 + 4
6 = 2 * 0 + 2 + 4
7 = 2 - 0! + 2 + 4
8 = 2 + 0 + 2 + 4
9 = 2 + 0! + 2 + 4
10 = 2 * (-(0!) + 2 + 4)
11 = 2 + 0! + 2 * 4
12 = 20 -(2 * 4)
13 = (2 + 0!)^2 + 4
14 = 20 - 2 - 4
15 = 20 - ([sqrt(2) + 4])
16 = 20 - [sqrt(24)]
17 = 20 + [sqrt(2)] - 4
18 = 20 + 2 - 4
19 = -2 - 0! - 2 +4!
20 = -[sqrt(20)] + 24
21 = -2 - 0! + 24
22 = -2 + 0 + 24
23 = -2 + 0! + 24
24 = 2 * 0 + 24
25 = 2 - 0! + 24
26 = 2 + 0 + 24
27 = 2 + 0! + 24
28 = 2 + 0 + 2 + 4!
29 = 2 + 0! + 2 + 4!

Here are K Sengupta's solutions:
0= [√20] - [√24]
1 = [√2] + 0! - 2 + [√(√(4))]
2 = [√2] + 0! - 2 + (√(4)
3 = 2+0!+2-√4
4 = [√2] + 0! - 2 + (4)
5= 2+0!-2+4
6 = 20/2 - 4
7 = 2+0+ [√2]+4
8= 2*0 + 2*4
9 = 2-0!+ 2"4
10 = 2*0!+2*4
11 = 2+0!+2*4
12 = [√202] - √4
13= [√202] - [√(√4)]
14 = 20/2 +4
15 = [√(202)] + [√(√4)]
16 = √(202)] + √4
17 = 20- 2 - [√(√4)]
18= 20 - 2 /[√√4]
19 = 20- 2/(√4)
20= 20+2 - √4
21 = 20+2/(√4)
22 = 20+2 - [√.4]
23 = 20+2 +[√√4]
24 = 20+2+√4
25 = 20+[(√2)] +4
26 = 20+2+4
27 = [√√√√√(20!)]+24
28 = 20 + 2*4
29 = -2-0+ [√2]+[√√√√(4!)!]
30 = 2+0-2 + [√√√√(4!)!]
31 = 2+0!-2+[√√√√(4!)!]
32 = 2+0!-[√2]+[√√√√(4!)!]
33 = [√20]-[ √2]+[√√√√(4!)!]
34 = [√20]-[ √.2]+[√√√√(4!)!]
35= [√20]+[ √2]+[√√√√(4!)!]
36 = [√20]+2+[√√√√(4!)!]
37 = [(√(20*2)]+[√√√√(4!)!]
38 = [√√√√(20!)]+ 24

Here are Kamal Lohia's solutions:
1 = (2+0+2)/4
2 = 2 × 0 - 2 + 4
3 = (2×0)! - 2 + 4
4 = (2×0×2) + 4
5 = (2×0×2)! + 4
6 = 20/2 - 4
7 = (2×0)! + 2 + 4
8 = 2 + 0 + 2 + 4
9 = (2×0)! + 2 × 4
10 = (20×2)/4
11 = (20+2)/√4
12 = (20/2) + √4
13 = (2 + 0!)² + 4
14 = (20/2) + 4
15 = -((2×0)!) + 2^4
16 = 2 × 0 + 2^4
17 = 2^0 + 2^4
18 = 2 + 0 + 2^4
19 = 2 + 0! + 2^4
20 = 20 + 2 - √4
21 = 20 + 2/√4
22 = 20 + √(2×√4)
23 = -((2×0)!) + 24
24 = 2 × 0 + 24
25 = (2×0)! + 24
26 = 2 + 0 + 24
27 = 2 + 0! + 24
28 = 2 + 0 + 2 + 4!
29 = 2 + 0! + 2 + 4!
30 = (2 + 0!)! + 24
31 = [√2] + (0! + 2)! + 4!
32 = 2 + (0! + 2)! + 4!
33 = (2 + 0!)² + 4!
34 = (20/2) + 4!
35 = (2 + 0!)!² - [√(√4)]
36 = (2 + 0!)! × 2 + 4!
37 = (2 + 0!)!² + [√(√4)]
38 = 20×2 - √4
39 = 20×2 - [√(√4)]
40 = 20×2×[√(√4)] = 20 ÷ .2 × 4
41 = 20×2 + [√(√4)]
42 = 20×2 + √4
43 = 20 - [√2] + 4!
44 = 20 + 24 = √20² + 4! = 20×2 + 4
45 = -2 - 0! + 2×4!
46 = -2 + 0 + 2×4!
47 = -2 + 0! + 2×4!
48 = 2×0 + 2×4!
49 = 2 - 0! + 2×4!
50 = 2 + 0 + 2×4!
51 = 2 + 0! + 2×4!
52 = 2×0!×(2 + 4!)
53 = [√(((2 + 0!)!)!)] × 2 + [√(√4)]
54 = (2 + 0!)! + 2 × 4!

Here are Davit Banana's solutions:


Click here to see Hari Kishan's solutions

For the third year in a row, Milos Vukovic has sent in 100 or more solutions (last year, he solved 1 to 216).
Here are his solutions for this year (he includes some explanations for some of the more complicated problems):

1 (2+0+2)/4
2 2*0-2+4
3 -(2+0)/2+4
4 2+0-2+4
5 (2+0)/2+4
6 2*0+2+4
7 2-0!+2+4
8 2*0+2*4
9 2-0!+2*4
10 2+0+2*4
11 2+0!+2*4
12 (2-0!+2)*4
13 [sqrt(2)]+(0!+2)*4
14 2+(0!+2)*4
15 (2+0!)*([sqrt(2)]+4)
16 (2+0+2)*4
17 20+[sqrt(2)]-4
18 20+2-4
19 20-2/sqrt(4)
20 20+2-sqrt(4)
21 20+2/sqrt(4)
22 -2+0+24
23 -2+0!+24
24 2*0+24
25 2-0!+24
26 2+0+24
27 2+0!+24
28 2+0+2+4!
29 2+0!+2+4!
30 (2-0!+2)!+4!
31 (2+0!)!+[sqrt(2)]+4!
32 (2+0)*(2^4)
33 (2+0!)^2+4!
34 20/2+4!
35 [20*2-sqrt(4!)]
36 20*2-4
37 [20*2-sqrt(sqrt(4!))]
38 20*2-sqrt(4)
39 20*2-[sqrt(sqrt(4))]
40 20*(-2+4)
41 [202/sqrt(4!)]
42 20*2+sqrt(4)
43 [20*2*sqrt(sqrt(sqrt(sqrt(4))))]
44 20+24
45 [2*(0-sqrt(2)+4!)]
46 2*(0!-2+4!)
47 [2*(0!-sqrt(2)+4!)]
48 (2+0!)*(2^4)
49 2-0!+2*4!
50 [202/4]
51 2+0!+2*4!
52 [2*(0!+sqrt(2)+4!)] 53 [sqrt(((2+0!)!)!)*(-2+4)]           expl     sqrt(720)*2
54 (2+0!)!+2*4!
55 [(sqrt(((2+0!)!)!)+[sqrt(2)])*sqrt(4)]           expl     (sqrt(720)+1)*2
56 [sqrt(202)]*4
57 [(sqrt(((2+0!)!)!)+2)*sqrt(4)]           expl     (sqrt(720)+2)*2
58 [sqrt(2)*sqrt(0!+2)*4!]
59 [2^((2+0!)!)-sqrt(4!)]           expl     2^6-sqrt(24)
60 20*(-[sqrt(2)]+4)
61 [2^((2+0!)!)-sqrt(sqrt(4!))]           expl     2^6-sqrt(sqrt(24))
62 2^((0!+2)!)-sqrt(4)           expl     2^6-2
63 2^((2+0!)!)-[sqrt(sqrt(4))]           expl     2^6-1
64 2^(0+2+4)
65 2^((0!+2)!)+[sqrt(sqrt(4))]           expl     2^6+1
66 2^((0!+2)!)+sqrt(4)           expl     2^6+2
67 [(2+0!)*(-sqrt(2)+4!)]           expl     3*(-1.41+24)
68 2^((0!+2)!)+4           expl     64+4
69 (2+0!)*(-[sqrt(2)]+4!)           expl     3*23
70 -2+(0!+2)*24
71 -[sqrt(2)]+(0!+2)*(4!)
72 (2+0!)*24
73 [sqrt(2)]+(0!+2)*(4!)
74 2+(0!+2)*24
75 [(20-sqrt(sqrt(2)))*4]
76 (20-[sqrt(2)])*4
77 [sqrt(((((2+0!)!)+[sqrt(2)])!)*sqrt(sqrt(sqrt(4))))]           expl     sqrt(7!*sqrt(sqrt(2)))
78 (2+0!)*(2+4!)
79 -2+(0!+2)^4           expl     -2+3^4
80 [(2+0!)*sqrt((2+4)!)]           expl     3*sqrt(720)
81 (2+0+[sqrt(2)])^4           expl     3^4
82 [sqrt(2)]+(0!+2)^4           expl     1+3^4
83 [sqrt(2)*sqrt((0!+2)!)*4!]
84 (20+[sqrt(2)])*4           expl     21*4
85 [(20+sqrt(2))*4]
86 [[sqrt(sqrt(sqrt(20!)))]/(sqrt(sqrt(sqrt(2)))+sqrt(sqrt(sqrt(4))))]
87 [sqrt(sqrt(sqrt(20!)))/(sqrt(sqrt(sqrt(2)))+sqrt(sqrt(sqrt(4))))]
88 (20+2)*4
89 [(2+sqrt(0!+2))*4!]
90 [2^((0!+2)!)*sqrt(sqrt(4))]           expl     2^6*sqrt(2)
91 202/(sqrt(sqrt(4!)))
92 [[sqrt(sqrt(sqrt(20!)))]/(sqrt(sqrt(sqrt(2)))+sqrt(sqrt(sqrt(sqrt(sqrt(4))))))]
93 [sqrt(((2+0!)!)!)*(-sqrt(2)+sqrt(4!))]           expl     sqrt(720)*(-sqrt(2)+sqrt(24))
94 [[sqrt(sqrt(sqrt(20!)))]/2/sqrt(sqrt(sqrt(sqrt(sqrt(4)))))]
95 [sqrt(sqrt(sqrt(20!)))/2/sqrt(sqrt(sqrt(sqrt(sqrt(4)))))]
96 ((2+0!)!)*(2^4)           expl     6*16
97 [sqrt(sqrt(sqrt(20!)))/2/sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(4))))))]
98 [([sqrt(((2+0!)!)!)]-sqrt(2))*4]           expl     (26-sqrt(2))*4
99 [([sqrt(((2+0!)!)!)]-sqrt(sqrt(2)))*4]           expl     (26-sqrt(sqrt(2)))*4
100 ([sqrt(((2+0!)!)!)]-[sqrt(2)])*4           expl     (26-1)*4
101 202/sqrt(4)


Correctly solved by:

1. Kamal Lohia     ** (54) Holy Angel School,
Hisar, Haryana, India
2. K. Sengupta     ** (38) Calcutta, India
3. Davit Banana     ** (25) Istanbul, Turkey
4. Dr. Hari Kishan     ** (28) D.N. College,
Meerut, Uttar Pradesh, India
5. Ivy Joseph     ** (30) Pune, Maharashtra, India
6. Milos Vukovic     ** (101) Budapest, Hungary
7. Colin (Yowie) Bowey     ** (30) Beechworth, Victoria, Australia
8. Kelly Stubblefield     ** (42) Mobile, Alabama, USA

      ** Extra Credit