Leaderboard
Minnesota
Rank
Level
1
Hakase
Minneapolis
95
2
Samantha Hallgren
Minneapolis
77
3
Yi L Lin
Minneapolis
57
4
User
Minneapolis
51
5
simon robert
Saint Paul
42
6
User
Saint Paul
42
7
User
East Grand Forks
40
8
User
Eagan
37
9
David Kloskin
Saint Paul
37
10
User
Rochester
37
11
Diane H.
Woodbury
36
12
User
Hopkins
34
13
User
Plymouth
34
14
Flej100
Minneapolis
33
15
User
Plymouth
33
16
krishnamoorthy dhanapal
Saint Paul
33
17
User
Shoreview
32
18
User
Mendota Heights
32
19
User
Minneapolis
31
20
User
Eden Prairie
31
21
User
Eden Prairie
29
22
User
Minneapolis
29
23
Ian Mark
Eden Prairie
28
24
Zachary Kriz
Mankato
28
25
User
Saint Paul
27
26
User
Northfield
26
27
User
Thief River Falls
26
28
User
Blaine
26
29
Bobby Meyer
Rochester
26
30
Carson Bynum
Edina
25
31
User
Saint Paul
25
32
User
Blaine
24
33
User
Minneapolis
24
34
User
Maple Grove
23
35
User
East Grand Forks
23
36
User
Minneapolis
23
37
User
Woodbury
23
38
User
Thief River Falls
22
39
Ian
Mankato
22
40
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Fairmont
21
41
kyle
Winnebago
21
42
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Edina
21
43
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Eden Prairie
21
44
User
Eden Prairie
21
45
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Eden Prairie
20
46
User
Hopkins
20
47
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Lakeville
20
48
User
Shoreview
20
49
User
Mankato
20
50
User
Minneapolis
20
51
kate moe
Saint Paul
20
52
Ca P
Minneapolis
20
53
User
Saint Paul
19
54
User
Fridley
19
55
User
Plymouth
19
56
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Bloomington
19
57
Pinchen Fan
Northfield
18
58
Alexandra
Brooklyn Park
18
59
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Edina
18
60
User
Shorewood
17
61
User
Maplewood
17
62
User
Minneapolis
17
63
User
Shorewood
17
64
User
Rochester
17
65
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Shoreview
17
66
User
Minneapolis
17
67
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Minneapolis
16
68
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Minneapolis
16
69
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Lakeville
16
70
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Saint Michael
16
71
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Saint Paul
16
72
User
Plymouth
15
73
User
Blaine
15
74
User
Minneapolis
15
75
User
Eden Prairie
15
76
User
Saint Anthony
14
77
User
Shoreview
14
78
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Roseau
14
79
User
Minneapolis
14
80
User
Chaska
13
81
User
Minneapolis
13
82
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Winona
13
83
User
Minneapolis
13
84
Adam Lemay
Minneapolis
13
85
mitch spack
Minneapolis
13
86
User
Winnebago
13
87
User
Saint Paul
13
88
User
Northfield
12
89
User
Andover
12
90
User
Minneapolis
12
91
Marat Bakpayev
Duluth
12
92
User
Saint Paul
12
93
User
Northfield
12
94
User
Eden Prairie
12
95
April Prchal
Eden Prairie
11
96
User
Eden Prairie
11
97
User
Minneapolis
11
98
User
Richfield
11
99
Joe
Minneapolis
11
100
User
Saint Paul
11
101
User
Golden Valley
11
102
User
Northfield
11
103
User
Northfield
11
104
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Pierz
10
105
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Saint Paul
10
106
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Northfield
10
107
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Minneapolis
10
108
Prakalya Krishnamoorthy
Saint Paul
10
109
User
Shakopee
10
110
Trisha
Eagan
10
111
User
Fridley
9
112
User
Minneapolis
9
113
User
Northfield
9
114
User
Minneapolis
9
115
User
Annandale
9
116
User
Minneapolis
9
117
Sophie Gorham
Minneapolis
9
118
rick kick
Maple Grove
8
119
User
Woodbury
8
120
User
Stillwater
8
121
User
Eagan
8
122
User
Minneapolis
8
123
User
Chaska
8
124
KATRIANA TRINH
Minnetonka
8
125
User
Eden Prairie
8
126
User
Minneapolis
7
127
User
Minnetonka
7
128
User
Saint Paul
7
129
User
Minneapolis
7
130
Liv Steen
Saint Louis Park
7
131
User
Chaska
7
132
User
Northfield
7
133
User
Northfield
7
134
User
Northfield
7
135
User
Edina
7
136
User
Lakeville
7
137
User
Minneapolis
7
138
User
Woodbury
7
139
User
Edina
7
140
User
Elko New Market
7
141
User
Minneapolis
7
142
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Bloomington
7
143
User
Minneapolis
7
144
User
Duluth
7
145
Jon Hasan
Winona
6
146
User
Bloomington
6
147
User
Minneapolis
6
148
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Edina
6
149
User
Bloomington
6
150
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Blaine
6
151
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Saint Paul
6
152
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Saint Paul
6
153
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Duluth
6
154
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Northfield
6
155
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Plymouth
6
156
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Dodge Center
6
157
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City
6
158
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Saint Paul
6
159
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Andover
6
160
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Minneapolis
6
161
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Mankato
6
162
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Minneapolis
6
163
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Golden Valley
6
164
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Moorhead
6
165
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Edina
6
166
Nil Borrell
Minneapolis
6
167
User
Minneapolis
6
168
Nevaeh Sibbert
Wadena
6
169
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Cottage Grove
6
170
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Eagan
6
171
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Minnetonka
6
172
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Fridley
6
173
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Plymouth
5
174
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Northfield
5
175
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Rochester
5
176
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West Saint Paul
5
177
User
Minneapolis
5
178
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Brooklyn Center
5
179
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Oakdale
5
180
User
Brooklyn Park
5
181
User
Minneapolis
5
182
User
Eagan
5
183
User
Maple Grove
5
184
User
Minneapolis
5
185
User
Minneapolis
5
186
Elsa
Minneapolis
5
187
Luis Tinoco
Minneapolis
5
188
User
Minneapolis
5
189
User
Minneapolis
5
190
User
Northfield
5
191
User
Northfield
5
192
User
Saint Paul
5
193
User
Richfield
5
194
User
Saint Paul
4
195
User
Shoreview
4
196
User
Mankato
4
197
User
Minneapolis
4
198
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Woodbury
4
199
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Minneapolis
4
200
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West Saint Paul
4
201
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Plymouth
4
202
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Apple Valley
4
203
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St. Louis Park
4
204
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Stewart
4
205
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Golden Valley
4
206
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Minneapolis
4
207
Connor Sanvik
Winona
4
208
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Minneapolis
4
209
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Brooklyn Park
4
210
User
Minneapolis
4
211
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Plymouth
4
212
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Northfield
4
213
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Northfield
4
214
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Northfield
4
215
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Saint Paul
4
216
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Minneapolis
4
217
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New Ulm
4
218
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Minneapolis
3
219
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Saint Paul
3
220
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Hutchinson
3
221
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Saint Paul
3
222
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Winona
3
223
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Maple Grove
3
224
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Eagan
3
225
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Mankato
3
226
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Minneapolis
3
227
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Saint Paul
3
228
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New Ulm
3
229
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Northfield
3
230
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Northfield
3
231
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Northfield
3
232
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Saint Louis Park
3
233
Miss Mathematics
Champlin
3
234
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Woodbury
3
235
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Ramsey
3
236
Gian Hernandez
Minneapolis
3
237
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Hopkins
3
238
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Woodbury
3
239
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Minneapolis
3
240
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Minneapolis
3
241
Alex Richardson
Saint Paul
3
242
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Le Sueur
2
243
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Fridley
2
244
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Golden Valley
2
245
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Edina
2
246
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Minneapolis
2
247
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Forest Lake
2
248
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Alexandria
2
249
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Minneapolis
2
250
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Chaska
2
251
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Edina
2
252
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Northfield
2
253
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Northfield
2
254
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Minnetonka
2
255
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Minneapolis
2
256
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Saint Charles
2
257
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Champlin
2
258
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Saint Paul
2
259
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Mankato
2
260
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Minneapolis
2
261
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2
262
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Minneapolis
2
263
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Eagan
2
264
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2
265
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2
266
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2
267
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2
268
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Blaine
2
269
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Minneapolis
2
270
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Minneapolis
2
271
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Plymouth
2
272
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Maplewood
2
273
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Minneapolis
2
274
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Winnebago
2
275
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2
276
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Minneapolis
2
277
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Alexandria
2
278
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279
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2
280
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2
281
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Minneapolis
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282
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283
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1
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285
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286
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287
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Lino Lakes
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292
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293
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294
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295
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296
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297
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298
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299
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1
300
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1
301
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302
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1
303
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Brooklyn Park
1
304
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Cambridge
1
305
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1
306
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South Saint Paul
1
307
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1
308
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1
309
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1
310
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1
311
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Minneapolis
1
312
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Duluth
1
313
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Duluth
1
314
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Winnebago
1
315
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Winnebago
1
316
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1
317
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1
318
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319
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320
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1
321
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324
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1
325
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326
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1
327
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1
328
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1
329
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330
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331
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332
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1
333
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334
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1
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1
336
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1
337
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1
339
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Shoreview
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1
341
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Shoreview
1
342
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1
343
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1
344
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366
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367
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368
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1
369
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A Web App for Mathematics Training

Do you want to be fast at mental math? Many people do, but the options for doing the necessary exercises are simply too cumbersome for all but the most dedicated of trainees. In physical fitness, many people are interested in training their bodies but allocating the time, energy, and money for it is a significant obstacle. Likewise, lugging around books and whatnot for math practice is a threshold that just doesn't meet the standards of modern life.

Training yourself to be skilled at mental math needs to be quick and convenient. mathtrainer.org is a web app that works in your browser rather than a program you have to download and install on your computer or phone. This allows users to try and use the app without having to install new software. As a web app, updates are also much simpler. There is no need to download endless updates—the website will always be the most current version.

You can access a web app from any device connected to the internet and equipped with a web browser, including smartphones, tablets, and desktop computers. Moreover, you are free to use whichever browser you prefer, including Google Chrome, Safari, Firefox, and others. Google Chrome is the recommended browser for the best maths training since it tends to lead the pack in supporting the latest web technologies.

Math Trainer is designed to offer a similar experience regardless of what you’re using to access it, whether it be Android, iOS, Windows, or another operating system. Though an on-screen touch keyboard will appear on mobile devices, you may prefer to use the app on a desktop with a keyboard. Hopefully the advantages of a web app for convenient mathematics training are apparent.

Another part of making the app easy to use is eliminating the need for signing up and logging in. Users can get started with their math training as soon as they click the start button on this page. After progressing to higher levels in the app, your progress is automatically saved so long as your return to the site through the same browser.


What's a Mental Math Tip?

A mental math tip is a sequence of steps that can be taken to solve a math problem in your head. Click the arrow below to see an example for the following problem:

÷
984
3
328

A tip like this one is available for every problem in Math Trainer, so there's always help if you get stuck. With enough math practice, you'll be able to predict what the tips will say—you'll have learned mental math!


Get Better at Mental Math

The ability to quickly perform mental calculations offers advantages in certain circumstances. But even without applications, getting better at mental math is a great way to stimulate one’s mind. It develops better number sense and intuition for quantifying the world around us. Practicing mental calculation will strengthen your foundation for learning more advanced maths topics.

Nonetheless, the tangible benefits of improving at mental math are many. It is certainly expected that educated people are able to do simple arithmetic without having to pull out a calculator. An inability to do so may reflect poorly on you, while being well-practiced in mental calculation will leave your contemporaries impressed. In many scientific and technical circles, mental math ability is even more highly regarded.

For students, mental calculation speed will often have a direct impact on math and science test scores. At all grade levels, it is not sufficient to know how to solve math problems when tests have a time limit on them. The highest-scoring test takers are able to answer questions both correctly and efficiently. Improving mental math skills will only benefit a student’s academic career.

Calculating the solution to an arithmetic problem in your head is often faster than pulling out a device to tell you the answer. For example, figuring out how much to tip a server at a restaurant is a straightforward arithmetic problem that many people are unable to perform without a calculator. By training your brain to solve basic math problems, you can save time in situations like these.

Mental math can also be relied upon when calculation devices are not available. Even with the conveniences of modern life, we occasionally find ourselves without access to our cell phones or other capable devices. A mind skilled in mental math is always available to you.

Finally, getting better at mental math enables a quick estimate and sanity check on results obtained from calculators. While computers are extremely reliable at solving math problems, there is always the risk of incorrectly inputting the problem to the computer. By getting better at mental mathematics, you will develop an intuition for whether the results of calculators make sense.

In fact, the ability to estimate is often sufficient to avoid using calculators altogether. While the use of computers is widespread, estimation is an increasingly valued skill in many industries. There are many situations where complex math will eventually be required, but a preliminary estimate is needed quickly. A major boost to productivity!


Use a Math Trainer

Mental math ability is a lot like physical fitness training. You may be out of shape in the beginning, but with diligent training you can and will improve. Initially you might not enjoy the exercise, but you will reap significant rewards for your effort. As you become more fit, you’ll begin to enjoy the activity much more. If you are serious about it, your mental calculation fitness could become a source of energy, galvanizing you to face the challenges of life with enthusiasm.

In physical training, you break down the fibers in your muscles during a workout session. Your muscles actually sustain tiny tears during resistance training exercises. While you rest afterwards, your body repairs the damage, rebuilding the fibers thicker and stronger.

A similar process is believed to occur for cognitive tasks. A 2016 study found "extensive evidence that brain-training interventions improve performance on the trained tasks".1 Therefore you can expect training your brain to answer mental math questions will lead to improved performance over time.

In the context of physical fitness, a "trainer" often refers to a trained professional who guides the workout and recovery process. Personal trainers are tasked with assessing a trainee's level of ability, prescribing an exercise regimen, and offering feedback as the training goes along. The word "trainer" could also refer to a system that automates the role of a personal trainer. Many aerobic exercise machines today offer interactive training programs with feedback and analysis of a user's performance.

A math trainer is needed for optimal math fitness. Like in physical fitness, the trainer should be compatible with users at a variety of skill levels and should guide them to the next level. It should give an accurate assessment of a user's strengths and weakness, as well as offer helpful feedback on where to focus one's efforts. Learning the ropes of mental maths with a math trainer should be a seamless, rewarding journey to ever-greater abilities.


Mental Calculation

Mental calculation, or mental math, is performing arithmetical calculations without the aid of tools or supplies. As opposed to using a calculator or pencil and paper, mental math is performed entirely in one’s head.

People use mental calculation when computation aides are not available, when it is faster to do so, or when they wish to practice math, show off, or participate in mental math competitions. Most people perform basic mental calculation using elementary arithmetic on a daily basis. An inability to calculate mentally is a serious obstacle to many common tasks.

In U.S. schools, mental calculation is taught only for the most elementary arithmetic, such as single-digit addition and multiplication of two numbers between 0 and 12. To solve addition problems involving multiple digits, you are taught to add columns of digits from right to left, carrying the tens digit if the column sum exceeds 9. For example, how would you approach this addition problem?

Example of two-digit
addition problem

If you were trained like many of us were, you’d add the right column to obtain 12. Since that’s two digits, you’d write the 2 under the right column and carry the 10 by writing a 1 above the left column. Finally, you’d add the two tens digits and the carried 1 to obtain the answer, 52.

To solve an addition problem mentally, it’s best to add the columns from left to right. In our example, you could add the tens digit of the second number, 30, to the first number, 14, to obtain 44. This is easier than the full problem because you’re just doing one mental calculation and tacking on the 4 from the 14 as the singles digit. Then you’d add the remaining ones digit of the second number, 8, to 44 to arrive at the answer, 52.

Which approach seems simpler to you? Can you do the first approach without pulling out a pencil and paper? It turns out the same advantages of left-to-right addition apply to much larger numbers as well. It’s unlikely that difficult addition problems can be solved right to left without needing to write it all out, which of course is more time consuming.

Mental math should be distinguished from the memorization of math facts such as multiplication tables. A foundation of memorized answers to simple math problems will make mental math easier, but performing maths in your head requires both memorized facts and the manipulation of numbers and operations to solve problems. This combination of skill and memory allows us to solve far more complex math questions than can be answered with readily-memorized math facts.

Many mental math tricks are specific to particular numbers or types of problems, usually dependent on the base of the number system used. In the decimal numeral system, for example, it is trivially easy to multiply by 10—just add a 0 to the end of the number. This mental math trick wouldn’t work in the hexadecimal numeral system, though, because the base is 16 instead of 10.

Therefore mental calculation is the ability to manipulate complex arithmetic problems in such a way that they can be resolved using simple memorized math facts.


Arithmetic

Arithmetic is the branch of mathematics concerning basic number operations: addition, subtraction, multiplication, and division. As kids, we are taught to do arithmetic because real-world math problems depend on a mastery of elementary arithmetic. Higher-level study of arithmetic and the integers, or whole numbers, is known as number theory.

Though the math kids initially study is arithmetic, the word is rarely used in this context anymore. Originally it comes from the Greek arithmos, meaning “number”. It has however been included in the “three Rs” of elementary Western education: reading, writing, and arithmetic.

There is evidence prehistoric humans were using arithmetic as hunter-gatherers. Archaeologists have uncovered a tally stick, believed to be over 20,000 years old, which may exhibit the earliest known sequences of prime numbers. An understanding of prime numbers, which are only divisible by themselves and the number 1, requires knowledge of the operation in arithmetic known as division.

From tally marks came base-10 numerals such as those used in Egypt over 5,000 years ago. Number systems based on 10 probably arose because humans have ten “digits” as fingers on their hands (or toes on their feet). A later advance in arithmetic was positional notation, which allowed the same symbols to represent different magnitudes depending on their position in the written number. These numeral systems allowed complex arithmetic to be communicated, recorded, and applied to the challenges faced by our ancestors.

The basic operation of arithmetic is addition. It combines two or more numbers into one, the sum of the terms. The terms can be added in any order, which is known as the commutative property of arithmetic. On a number line, the sum of two numbers is the total distance from zero covered by both numbers.

The inverse arithmetical operation of addition is subtraction. It finds the difference between two numbers. Subtraction is not commutative because the order of the numbers determines whether the answer is positive or negative. On a number line, the difference between two numbers is the distance between their positions.

A second basic operation of arithmetic is multiplication, which scales a number by another number. This second number is called a factor. Like addition, multiplication is commutative—you can change the order of the factors and still get the same answer. Multiplication on a number line can be viewed as adding the first number a total number of times equal to the second factor.

Finally, division is an arithmetical operation that is essentially the inverse of multiplication. Rather than scaling a number, it is divided into a number of pieces equal to the second number. Dividing by the number 0 is not defined in arithmetic because dividing something into zero pieces is impossible.

Basic arithmetic allows us to evaluate the answers to an unlimited number of mathematical expressions. Arithmetical expressions can be purely mathematical, as in 2 + 2, or they can represent quantities in the physical world, such as two items plus two more. Understanding the laws of arithmetic is tremendously powerful.


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