Leaderboard
India
India
Worldwide
Rank
Level
1
Sandeep
Rajasthan
100
2
User
Delhi
99
3
Rajaram
West Bengal
98
4
Abhishek Singh
West Bengal
98
6
Dhruv Arora
Punjab
94
9
MyNameIsMe
Telangana
91
10
Narasimha
Karnataka
91
11
User
West Bengal
90
12
User
Maharashtra
90
13
velidi murali krishna
Telangana
89
14
User
Goa
87
15
User
West Bengal
85
17
User
Bihar
84
18
User
Bihar
84
19
User
West Bengal
84
20
Abhilash IITP
Bihar
84
21
Vivek Nautiyal
Karnataka
83
22
Bipin Bihari che15(IIT bhu)
Uttar Pradesh
83
23
User
Maharashtra
82
24
shubham bansal
Maharashtra
82
25
ajinkya awachar
Madhya Pradesh
82
26
User
Maharashtra
81
27
User
Maharashtra
81
28
User
Bihar
80
29
User
Maharashtra
80
30
User
Telangana
80
32
Monica
Maharashtra
79
33
Jagat
Karnataka
78
35
User
Bihar
78
36
User
Gujarat
78
37
Rakesh Singh
West Bengal
78
38
User
Rajasthan
77
39
User
Rajasthan
77
40
Ankit Ahuja
Delhi
77
41
Sai Jahnavi Yeruva
Karnataka
76
42
User
Maharashtra
76
43
Jayasheelli k
Karnataka
76
44
User
Bihar
76
45
User
Kerala
76
46
Mahesh Kanade
Madhya Pradesh
76
47
User
West Bengal
76
48
User
Gujarat
76
49
User
Tamil Nadu
75
50
User
Karnataka
75
51
GitGud
Karnataka
75
52
Hari Sankar Narayanan
Tamil Nadu
75
53
MUKILA M
Tamil Nadu
75
54
Tejas ___
Maharashtra
74
55
Tejas
Maharashtra
74
56
User
Bihar
74
57
User
Maharashtra
74
58
Sumant Kumar
Tamil Nadu
74
59
User
Maharashtra
73
60
User
Bihar
73
61
User
Bihar
73
62
User
Maharashtra
72
63
Surya Narayan Sen
West Bengal
72
64
User
Delhi
71
65
User
Maharashtra
70
66
Sharan
Chandigarh
70
67
User
Maharashtra
70
68
User
Maharashtra
69
69
hotessy
Delhi
69
70
User
Tamil Nadu
69
71
User
Maharashtra
69
73
bigblackclock
Karnataka
68
74
User
Bihar
68
75
User
Punjab
67
76
User
Goa
67
77
User
Maharashtra
67
78
KSingh
Karnataka
66
79
User
Kerala
66
80
User
Bihar
66
81
User
Maharashtra
66
84
User
West Bengal
66
85
Arjit Kapoor
Delhi
66
86
Soumya
Uttar Pradesh
65
87
User
Maharashtra
65
88
User
West Bengal
65
89
User
Maharashtra
65
90
Raghav Dhawan
Andhra Pradesh
65
91
User
Maharashtra
65
92
Arham Kothari
Telangana
64
93
User
Maharashtra
64
94
User
Bihar
64
95
User
Bihar
64
96
User
Tamil Nadu
64
98
User
Maharashtra
64
99
User
Tamil Nadu
63
100
User
Uttar Pradesh
63
101
CHITRANGAD
West Bengal
63
102
Dishank Agrawal
West Bengal
63
103
User
Maharashtra
63
104
User
Chandigarh
63
106
Divya Goel
Delhi
62
107
Abhishek Manwani
Madhya Pradesh
62
108
Rahul Godara
Delhi
62
109
User
West Bengal
62
110
John Louis
Tamil Nadu
62
111
Shaurya Vijay
Bihar
62
112
Aarya Singh
Uttar Pradesh
62
113
User
Delhi
62
114
User
Delhi
62
115
User
Telangana
62
116
User
Chandigarh
62
117
Sai Yashwanth
Telangana
62
118
User
Odisha
62
119
SidMan
Maharashtra
61
120
User
Rajasthan
61
121
Soumya
Uttar Pradesh
61
122
Vedavyas
Haryana
61
123
User
Delhi
61
124
Priyanshu Gupta
Karnataka
61
125
User
Maharashtra
61
126
User
Tamil Nadu
61
127
babnish19
Bihar
61
128
User
Maharashtra
61
129
User
Tamil Nadu
61
130
User
West Bengal
61
131
Pratik Kumar
Delhi
61
132
krishna bhati
Rajasthan
60
133
User
West Bengal
60
134
User
Karnataka
60
136
User
West Bengal
60
137
User
Maharashtra
60
138
User
Bihar
60
139
User
Tamil Nadu
59
140
User
West Bengal
59
141
User
West Bengal
59
142
Kolisettiramalingam Ramalingam
Tamil Nadu
59
143
Adarsh Verma
Uttar Pradesh
59
145
User
West Bengal
58
146
Abhyuday Sharma
Rajasthan
58
147
cbzsports1098
Maharashtra
58
148
User
Maharashtra
58
149
Vikrant Shah
Maharashtra
58
150
User
Haryana
57
151
User
Delhi
57
152
User
Maharashtra
57
153
User
Maharashtra
57
154
Sankalp Krishnan
Maharashtra
57
155
a a
Maharashtra
57
156
Sandhya Naik
Karnataka
57
157
Sandhya
Karnataka
57
158
User
Delhi
56
159
User
Chhattisgarh
56
160
Sachin kumar Gupta
Madhya Pradesh
56
161
User
West Bengal
56
162
User
West Bengal
56
163
User
Kerala
56
164
User
Maharashtra
56
165
User
Tamil Nadu
56
166
aman rathore
Uttar Pradesh
56
167
Gauransh
Uttar Pradesh
56
168
User
West Bengal
56
169
ANKIT SANKHALA
Rajasthan
55
170
User
Maharashtra
55
171
Akhila Vijayan
Kerala
55
172
User
Maharashtra
55
173
User
West Bengal
55
174
Mohit Singhal
Madhya Pradesh
54
175
Jeevottam Bhat
Karnataka
54
176
Tejaswi B
Telangana
54
177
User
Bihar
54
178
User
Uttar Pradesh
54
179
User
Rajasthan
54
181
User
Karnataka
54
182
Shree
Maharashtra
54
183
User
Delhi
54
184
Yousef c t
Kerala
53
185
User
Chhattisgarh
53
186
User
West Bengal
53
187
User
Maharashtra
53
188
User
West Bengal
53
189
User
West Bengal
53
190
User
Maharashtra
53
191
User
Bihar
53
192
User
West Bengal
53
193
Parismita Das
Assam
53
194
Aasif Anis
Delhi
53
195
User
Delhi
53
196
NARENDRA AGRAWAL
Andhra Pradesh
53
197
User
Rajasthan
53
198
SHUBHAM KUMAR
Bihar
53
199
User
Maharashtra
53
200
User
Tamil Nadu
52
201
Duke Das
Karnataka
52
202
User
Rajasthan
52
203
User
Maharashtra
52
204
PRADEEP KUMAR
Telangana
52
205
User
Rajasthan
52
206
User
Tamil Nadu
52
207
User
Telangana
52
208
User
Odisha
52
209
User
Kerala
52
210
User
Maharashtra
52
211
User
West Bengal
52
212
User
Odisha
52
213
User
Delhi
52
214
User
Maharashtra
52
216
Soham Gupta
Gujarat
51
217
Adarshdeep Singh
Karnataka
51
218
Keshav
Haryana
51
219
Prerna Pahwa
Delhi
51
220
User
Karnataka
51
221
User
Telangana
51
223
User
West Bengal
51
224
User
Gujarat
51
225
Prem Agrawal
Maharashtra
51
226
User
Maharashtra
51
227
Yedukrishnan P
Maharashtra
51
228
User
West Bengal
51
229
Harpreet Bagga
Uttar Pradesh
51
230
User
Rajasthan
51
232
Preet Khalsa
Rajasthan
50
233
User
Gujarat
50
234
User
Maharashtra
50
237
User
Jharkhand
50
238
User
West Bengal
50
239
User
Tamil Nadu
50
240
User
Maharashtra
50
241
User
Tamil Nadu
50
242
User
Uttar Pradesh
50
243
User
Haryana
50
244
User
Karnataka
50
245
User
West Bengal
50
246
Soumitra Chattopadhyay
Maharashtra
50
247
bheesetti rajkumar
Andhra Pradesh
50
248
Abhiraj Aditya
West Bengal
50
249
User
Maharashtra
49
250
User
Maharashtra
49
251
User
Karnataka
49
252
User
Rajasthan
49
253
User
Gujarat
49
254
User
Uttar Pradesh
49
255
User
Delhi
49
256
User
Bihar
49
257
User
Tamil Nadu
49
258
User
Punjab
49
259
User
Maharashtra
49
260
User
Uttar Pradesh
49
261
Ankur Kothari
Rajasthan
49
262
User
Maharashtra
49
263
User
Chhattisgarh
49
264
Anuraag Kunchala
Uttar Pradesh
49
265
Harsh Sarda
Haryana
49
266
anshul sahu
Madhya Pradesh
49
267
Apurva Bomanwar
Kerala
49
268
Arka Provo Mukhopadhyay
Rajasthan
49
269
User
Haryana
48
270
User
Telangana
48
271
RP Gaur
Uttar Pradesh
48
273
Sairam Sablo
Tamil Nadu
48
274
User
Gujarat
48
275
Meghana
Maharashtra
48
276
User
Maharashtra
48
277
User
Tamil Nadu
48
278
Cannibal Hamster
Telangana
48
279
User
Delhi
48
280
User
Delhi
48
281
User
Maharashtra
48
282
User
Maharashtra
48
283
User
Uttar Pradesh
48
284
User
Tamil Nadu
48
285
madhu mitha
Tamil Nadu
48
286
axolotl-man
Karnataka
47
287
User
Karnataka
47
289
User
Tamil Nadu
47
290
User
Karnataka
47
291
User
Uttar Pradesh
47
292
User
Bihar
47
293
kamal
Rajasthan
47
294
User
Maharashtra
47
295
User
Maharashtra
47
296
User
Maharashtra
47
297
Aakarsh Chauhan
Assam
47
298
RICK
Uttar Pradesh
47
299
User
Uttar Pradesh
47
300
User
Delhi
47
301
User
West Bengal
47
302
User
Bihar
47
303
User
Tamil Nadu
47
304
Jagjit Singh
West Bengal
46
305
Akriti Verma
Jammu and Kashmir
46
306
User
Chhattisgarh
46
307
User
West Bengal
46
308
User
Uttar Pradesh
46
309
User
Tamil Nadu
46
311
User
Maharashtra
46
312
User
Uttar Pradesh
46
313
User
Delhi
46
314
User
Karnataka
46
315
User
West Bengal
46
316
User
Odisha
46
317
User
Bihar
46
318
User
Delhi
46
319
User
Maharashtra
46
320
User
Telangana
46
321
User
West Bengal
46
322
User
Tamil Nadu
46
323
User
Rajasthan
46
324
User
Karnataka
46
325
User
Tamil Nadu
46
326
User
Delhi
45
327
User
Odisha
45
328
User
Kerala
45
329
User
West Bengal
45
330
User
Haryana
45
331
User
Bihar
45
332
Charvi Singh
Delhi
45
334
User
Uttar Pradesh
45
335
User
Delhi
45
336
User
Maharashtra
45
337
User
Kerala
45
338
User
Odisha
45
339
MANISH PANDEY
Bihar
45
340
User
West Bengal
45
341
Divyansh Gupta
Delhi
45
342
User
Maharashtra
45
343
User
Uttar Pradesh
45
344
Kaustubh Bhoir
Maharashtra
45
345
User
Delhi
45
346
User
Maharashtra
45
347
ANIL KUMAR KUMAWAT
Rajasthan
44
348
User
West Bengal
44
349
User
Telangana
44
350
User
Maharashtra
44
351
User
Bihar
44
352
User
Maharashtra
44
353
Pranjali
Gujarat
44
354
User
Maharashtra
44
355
User
Telangana
44
356
User
Delhi
44
357
User
Maharashtra
44
358
User
Maharashtra
44
359
wolf_001
Delhi
44
360
shubham gupta
Karnataka
44
361
vikrant singh
Delhi
44
362
User
Jharkhand
44
363
User
Bihar
44
364
User
Uttar Pradesh
44
365
User
Bihar
44
366
User
Karnataka
44
367
SHASHWATA NAYAK
Odisha
43
368
User
Tamil Nadu
43
369
User
Maharashtra
43
370
User
Kerala
43
371
User
Karnataka
43
372
User
Tamil Nadu
43
373
User
Kerala
43
374
Nipun Kanade
Tamil Nadu
43
375
User
Maharashtra
43
376
User
Telangana
43
377
User
Haryana
43
378
User
Maharashtra
43
379
User
Uttarakhand
43
380
User
Tamil Nadu
43
381
User
Karnataka
43
382
User
Maharashtra
43
383
User
Maharashtra
43
384
User
Tamil Nadu
43
385
User
Rajasthan
43
386
User
West Bengal
43
387
User
Maharashtra
43
388
secret agent
Assam
43
389
User
Gujarat
43
390
Lenin Sundaram
Tamil Nadu
43
391
User
West Bengal
42
392
User
Tamil Nadu
42
394
User
Haryana
42
395
User
Tamil Nadu
42
396
User
Tamil Nadu
42
397
Sandeep
Uttar Pradesh
42
398
User
Maharashtra
42
399
User
Telangana
42
400
User
Delhi
42
401
User
Uttar Pradesh
42
402
karthikeya
Telangana
42
403
LoLwa
Delhi
42
404
User
Delhi
42
405
User
Maharashtra
42
406
furqan suleman
Maharashtra
42
407
User
Telangana
42
408
User
Maharashtra
42
409
User
Karnataka
42
410
User
Maharashtra
42
411
User
Maharashtra
42
412
User
Maharashtra
42
413
User
Karnataka
42
414
User
Bihar
42
415
User
Delhi
42
416
User
Odisha
42
417
Mohammed Bilal Girach
Assam
42
419
User
Gujarat
42
420
User
Tamil Nadu
42
421
User
Delhi
42
422
Ashutosh Kale
Haryana
41
423
User
Karnataka
41
424
Sneh Goel
Delhi
41
425
AMAN TIWARI
West Bengal
41
426
User
Maharashtra
41
427
Sayo Sayo
Bihar
41
428
User
Telangana
41
429
User
Maharashtra
41
430
User
Delhi
41
431
User
Delhi
41
432
User
Delhi
41
433
User
Delhi
41
434
User
Maharashtra
41
435
User
Maharashtra
41
436
User
Karnataka
41
437
User
Karnataka
41
438
User
Maharashtra
41
439
User
Karnataka
41
440
Aarif Shaikh
Maharashtra
41
441
Pritisha Biswas
Odisha
41
442
User
West Bengal
41
443
User
West Bengal
41
444
User
West Bengal
41
445
User
Tamil Nadu
41
446
User
Maharashtra
41
447
User
West Bengal
41
448
User
West Bengal
41
449
Manoj Singhi
Delhi
41
450
Abhishek Singh
Bihar
41
451
Fawaz Wangde
Maharashtra
41
452
Sumeet Pannu
Delhi
41
453
User
Tamil Nadu
41
454
User
Delhi
41
455
User
Uttar Pradesh
40
456
User
Maharashtra
40
457
User
Tamil Nadu
40
458
User
Telangana
40
459
User
Goa
40
460
User
West Bengal
40
461
User
Delhi
40
462
User
Kerala
40
463
User
Tamil Nadu
40
464
User
Maharashtra
40
465
User
Tamil Nadu
40
466
User
Maharashtra
40
467
Abhishek Salve
Karnataka
40
468
User
Karnataka
40
469
User
Maharashtra
40
470
User
Maharashtra
40
471
User
Karnataka
40
472
User
Delhi
40
473
User
Maharashtra
40
474
User
Maharashtra
39
475
vratant GUPTA
Delhi
39
476
Muni Bhaskar
Tamil Nadu
39
477
User
West Bengal
39
478
User
Maharashtra
39
479
VijayG
Karnataka
39
480
User
Uttarakhand
39
481
User
Tamil Nadu
39
482
User
Delhi
39
483
User
Telangana
39
484
User
Bihar
39
485
User
Tamil Nadu
39
486
User
Uttar Pradesh
39
487
Ashutosh Singhania
Uttar Pradesh
39
488
User
Maharashtra
39
489
User
Gujarat
39
490
shrey jain
Maharashtra
39
491
User
Telangana
39
493
User
Uttarakhand
39
494
User
West Bengal
39
495
User
Assam
39
496
User
Tamil Nadu
39
497
User
Maharashtra
39
498
User
Bihar
39
499
digvijay kodi
Assam
39
500
User
Bihar
39
501
User
Delhi
39
502
User
Karnataka
39
503
User
Rajasthan
39
504
User
Karnataka
38
506
User
Maharashtra
38
507
User
Gujarat
38
509
User
Bihar
38
510
Prativa Das
West Bengal
38
511
User
Telangana
38
512
Medha Chandra
Delhi
38
513
User
Delhi
38
514
User
Tamil Nadu
38
515
User
Maharashtra
38
516
User
Tamil Nadu
38
517
User
Jharkhand
38
519
Tarun Singh
Karnataka
38
520
User
Delhi
38
521
User
Jharkhand
38
522
Pratik Acharya
Maharashtra
38
524
User
Telangana
38
525
User
West Bengal
38
526
User
West Bengal
38
528
User
Delhi
38
529
User
Karnataka
38
530
User
Delhi
38
531
User
Delhi
38
532
User
Tamil Nadu
38
533
User
Delhi
38
534
User
Maharashtra
37
535
User
Delhi
37
536
User
Gujarat
37
537
User
West Bengal
37
538
User
Tamil Nadu
37
539
Shubhayan Kabir
Maharashtra
37
540
User
West Bengal
37
541
User
Maharashtra
37
542
User
Gujarat
37
544
User
Delhi
37
545
User
West Bengal
37
546
User
West Bengal
37
547
User
Karnataka
37
548
Ajay Verma
Uttar Pradesh
37
549
ajay singh thakur
Madhya Pradesh
37
550
User
Maharashtra
37
551
User
Puducherry
37
552
User
Karnataka
37
553
User
Delhi
37
554
User
Maharashtra
37
555
User
Delhi
37
556
User
Maharashtra
37
557
User
Uttarakhand
37
558
User
Haryana
37
559
User
Telangana
37
560
User
West Bengal
37
561
User
Tamil Nadu
37
562
User
Uttar Pradesh
37
563
User
Odisha
37
564
User
Uttar Pradesh
37
565
User
West Bengal
37
566
Trust My Tips
Rajasthan
37
567
User
Maharashtra
37
568
User
Tamil Nadu
36
569
User
Karnataka
36
570
User
Rajasthan
36
571
User
Delhi
36
572
Mohit Garg
Telangana
36
573
User
Karnataka
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575
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Gujarat
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576
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Maharashtra
36
577
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578
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36
579
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Haryana
36
580
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36
581
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582
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36
583
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Tamil Nadu
36
584
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Uttar Pradesh
36
585
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36
586
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Maharashtra
36
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36
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Tamil Nadu
36
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Maharashtra
36
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Tamil Nadu
36
591
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Telangana
36
592
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West Bengal
36
593
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Maharashtra
36
594
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Uttar Pradesh
36
595
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West Bengal
36
596
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Madhya Pradesh
36
597
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Delhi
36
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36
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Kerala
36
600
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Haryana
36
601
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36
602
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36
603
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604
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35
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legend killer
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35
606
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Maharashtra
35
607
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35
608
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Chhattisgarh
35
609
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610
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611
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Maharashtra
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613
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Maharashtra
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Telangana
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Haryana
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Maharashtra
35
619
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621
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Maharashtra
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622
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Maharashtra
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628
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Delhi
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630
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Maharashtra
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Maharashtra
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Maharashtra
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15TUCV053 THEEPAK A.
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Maharashtra
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1000
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Maharashtra
27

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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 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, 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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