January 2026
Problem of the Month

The New Year Challenge

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, 6, (and in that order) along with the operations listed above to write expressions for all the numbers from 1 to 26.

Extra credit for those who can go past 26 (consecutively).

Click here for a worksheet

Click here for solutions to previous years

Some Solutions to the Problem:

Here are Colin Bowey's answers:
1 =-2-FACT(0)-2+6
2 =-2-0-2+6
3 =-2+FACT(0)-2+6
4 =2*0-2+6
5 =2-FACT(0)-2+6
6 =(2*0*2)+6
7 =2+FACT(0)-2+6
8 =(2*0)+2+6
9 =2-FACT(0)+2+6
10 =2+0+2+6
11 =2+FACT(0)+2+6
12 =2*0+2*6
13 =2-FACT(0)+(2*6)
14 =2+0+(2*6)
15 =((2+FACT(0))^2)+6
16 =(2+0)*(2+6)
17 =INT(20-SQRT(2+6))
18 =(2-FACT(0)+2)*6
19 =INT((SQRT(SQRT(2)+0)+2)*6)
20 =2+(FACT(0)+2)*6
21 =20+INT(SQRT(SQRT(2*SQRT(6))))
22 =INT(20+(SQRT(2+SQRT(6))))
23 =-2-FACT(0)+26
24 =(2+0+2)*6
25 =-2+FACT(0)+26
26 =2*0+26
27 =INT(20+SQRT(2)+6)
28 =2+0+26
29 =2+FACT(0)+26
30 =(2+FACT(0)+2)*6
31 =2+FACT(0)+2+INT(SQRT(FACT(6)))
32 =FACT(2+FACT(0))+26
33 =INT(202/6)
34 =20*2-6
35 =INT(SQRT(20*(2^6)))
36 =(2+FACT(0))*2*6
37 =INT(SQRT((2^0)*2*FACT(6)))
38 =INT((SQRT(20)+2)*6)
39 =INT((INT(SQRT(20))^2)*SQRT(6))
40 =INT(2^FACT(FACT(0)+2)/SQRT(SQRT(6)))
41 =20*2 + INT(SQRT(SQRT(6)))
42 =FACT(2+FACT(0))^2+6
43 =(20*2)-INT(-(SQRT(6)))
44 =20-2+INT(SQRT(FACT(6)))
45 =INT(SQRT(2+FACT(0))*26)
46 =20*2+6
47 =20-INT(-(SQRT(2+FACT(6))))
48 =(2^(FACT(0)+2))*6
49 =-INT(-(FACT(2+FACT(0)+2)/SQRT(6)))
50 =2*(-FACT(0)+26)
51 =INT(2^FACT(FACT(0)+2)/SQRT(SQRT(SQRT(6))))
52 =(2^0)*2*INT(SQRT(FACT(6)))
53 =INT(SQRT(20)*2*6)
54 =2*(FACT(0)+26)
55 =2+0+INT(2*SQRT(FACT(6)))
56 =INT(20*SQRT(2+6))
57 =-INT(-20*SQRT(2+6))
58 =2^FACT(FACT(0)+2)-6
59 =INT(-SQRT(20)) + 2^6
60 =FACT(2+FACT(0)+2)/INT(SQRT(6))
61 =INT(2^FACT(FACT(0)+2)-SQRT(6))
62 =INT((SQRT(2)+FACT(0))*26)
63 =2^FACT(FACT(0)+2) - INT(SQRT(SQRT(6)))
64 =2^(FACT(FACT(0)+2))
65 =2^FACT(FACT(0)+2) + INT(SQRT(SQRT(6)))
66 =INT(20^2/6)
67 =2^FACT(FACT(0)+2) - INT(-SQRT(6))
68 =INT(SQRT(20)) + 2^6
69 =INT(20*SQRT(2*6))
70 =FACT(2+FACT(0))+2^6
71 =INT(20*(2+SQRT(SQRT(6))))
72 =FACT(2+FACT(0))*(2*6)
73 =INT(2*(-FACT(0)+SQRT(2*FACT(6))))
74 =2*INT(0+SQRT(2*FACT(6)))
75 =INT(2*SQRT((0+2)*FACT(6)))
76 =INT((SQRT(SQRT(20-2)))^6)
77 =INT(20*(SQRT(2)+SQRT(6)))
78 =(2+FACT(0))*26
79 =INT(FACT(-INT(-SQRT(20))) / SQRT(SQRT(SQRT(26))))
80 =20*(-2+6)
81 =(2+FACT(0))^(2+INT(SQRT(6)))
82 =INT(202/SQRT(6))
83 =-INT(-202/SQRT(6))
84 =20+2^6
85 =INT(SQRT(202)*6)
86 =-INT(-(SQRT(202)*6))
87 =INT(20 / SQRT(SQRT(2/FACT(6))))
88 =INT(20*(2+SQRT(6)))
89 =-(INT(20*(-2-SQRT(6))))
90 =2^FACT(FACT(0)+2) + INT(SQRT(FACT(6)))
91 =INT(20*(-SQRT(2)+6))
92 =-INT(20*(SQRT(2)-6))
93 =FACT(2+FACT(0)+2) + INT(-SQRT(FACT(6)))
94 =FACT(2+FACT(0)+2) - INT(SQRT(FACT(6)))
95 =INT((2+FACT(0))*SQRT(SQRT(2)*FACT(6)))
96 = INT(20*(-SQRT(SQRT(2))+6))
97 =INT(20*2*SQRT(6))
98 =INT(20*(-SQRT(SQRT(SQRT(2)))+6))
99 = INT(20*(-SQRT(SQRT(SQRT(SQRT(2))))+6))
100 =20*INT(SQRT(26))
101 =INT(202/INT(SQRT(6)))
102 =-INT(-20*SQRT(26))
103 =INT(SQRT(SQRT(20+2))^6)
104 =INT((INT(SQRT(20)))*(26))
105 =INT(20*SQRT(2+(INT(SQRT(FACT(6))))))
106 =(2+0)*(INT((2)*(SQRT(FACT(6)))))
107 =INT((2+0)*2*SQRT(FACT(6)))
108 =(20-2)*6
109 =INT(2*(FACT(0)+2*(SQRT(FACT(6)))))
110 =INT(20/(SQRT(SQRT(SQRT(2)))/6))
111 =INT((20-SQRT(2))*6)
112 =INT((20-SQRT(SQRT(2)))*6)
113 =INT(SQRT((20-2)*(FACT(6))))
114 =(20-INT(SQRT(2)))*6
115 =INT(SQRT((20-(SQRT(2)))*(FACT(6))))
116 =INT(SQRT(20)*26)
117 =-INT(SQRT(20)*-26)
118 =-2+FACT(INT(SQRT(26)))
119 =-(2^0)+FACT(INT(SQRT(26)))
120 =INT((SQRT(20)^2)*6)
121 =(2^0)+FACT(INT(SQRT(26)))
122 =2+FACT(INT(SQRT(26)))
123 =INT(20*SQRT(SQRT(2*FACT(6))))
124 =INT(SQRT((20+SQRT(2))*FACT(6)))
125 =INT((SQRT(20)/2)^6)
126 =INT((20+(INT(SQRT(2))))*6)
127 =INT((20+SQRT(SQRT(2)))*6)
128 =(2+0)*(2^6)
129 =INT(202/SQRT(SQRT(6)))
130 =2*(FACT(0)+(2^6))
131 =INT(SQRT(FACT(2+2)*(FACT(6))))
132 =(20+2)*6
133 =INT(-(20^2)/INT(-SQRT(6)))
134 =-INT((20^2)/INT(-SQRT(6)))
135 =INT(SQRT(SQRT(20))*(2^6))
136 =-INT(-SQRT(SQRT(20))*(2^6))
137 =INT(SQRT(INT(20*(SQRT(2))))*INT(SQRT(FACT(6))))
138 =INT(20*SQRT(SQRT(2)))*6
139 =INT(SQRT((INT(SQRT(20))+(SQRT(SQRT(2)))))^6)
140 =20*(INT(SQRT(2))+6)
141 =INT(20*((SQRT(SQRT(SQRT(2))))+6))
142 =INT(20*(SQRT(SQRT(2))*6))
143 =INT(20*(SQRT(SQRT(2))+6))
144 =FACT(2+2)*6
145 =INT(20*SQRT(INT(2*SQRT(FACT(6)))))
146 =INT(20*SQRT(2*SQRT(FACT(6))))
147 =-INT(-20*SQRT(2*SQRT(FACT(6))))
148 =INT(20*(SQRT(2)+6))
149 =-INT(-20*(6+SQRT(2)))
150 =(INT(-SQRT(20))^2)*6

Click here for Davit Banana's solutions

Click here for Hari Kishan's solutions

Click here for Kamal Lohia's solutions

Click here for David Mark's solutions

Click here for Ivy Joseph's solutions

Click here for Ievgen Murzak's solutions
This file opens in Excel and uses Reversed Polish Notation (RPN)
For example, 2 0 + 2 ! - 6 * would mean
((2 + 0) - (2!)) * 6 = 0.

Click here for Sevana Sarraf's solutions

Correctly solved by:

1. Kamal Lohia   ** (solved 32 consecutively)	Hisar, Haryana, India
2. Dr. Hari Kishan   ** (solved 30 consecutively)	D.N. College, Meerut, Uttar Pradesh, India
3. Colin (Yowie) Bowey   ** (solved 150 consecutively)	Beechworth, Victoria, Australia
4. Davit Banana   ** (solved 42 consecutively)	Istanbul, Turkey
5. David Marks   ** (solved 30 consecutively)	San Mateo, California, USA
6. Ivy Joseph   ** (solved 28 consecutively)	Pune, Maharashtra, India
7. Ievgen Murzak   ** (solved 122 consecutively)	Kyiv, Ukraine
8. Sevana Sarraf   ** (solved 30 consecutively)	Lebanon

      ** Extra Credit

Send any comments or questions to: David Pleacher