Leaderboard
United Kingdom
United Kingdom
Worldwide
Rank
Level
1
Matthew peters
England
100
2
Tom Scotney
England
99
3
User
England
97
4
Aarush
England
96
5
Marcus Hodgart
England
95
6
Santa Claus
England
95
7
Sean McCarthy
England
93
9
Shrootz
England
88
10
User
England
87
11
WhiteFalcon
England
87
12
User
England
86
13
User
England
82
14
User
England
82
15
B l
England
82
16
Petr Novák
England
79
17
User
Scotland
78
18
Christopher Dick
England
77
19
User
England
76
20
User
Scotland
76
21
ChainLink
England
75
22
User
England
75
23
Frank Burton
England
75
24
Jonathan
England
74
25
Alexander Zhang
Scotland
74
26
User
England
74
27
Looking for a Junior Trader position: sacha.di-martino18@imperial.ac.uk
England
73
28
Anais Deere
Wales
73
29
User
England
72
30
Natalie Wall
England
71
31
User
England
71
32
User
England
70
33
Siddhant Manchanda
England
70
34
Muhamed Ashiq
England
69
35
User
England
68
36
Simi Chavda
England
68
37
User
England
68
38
Andrei Puspana
England
67
39
Reggie Bains
England
67
40
Zohaib
England
66
41
Michalis
England
65
42
User
England
65
43
User
England
65
44
User
England
65
45
Nithil Kennedy
England
65
46
The Master Procrastinator
England
64
47
Ghadi
England
64
48
User
England
64
49
User
England
64
50
User
England
63
51
User
England
63
52
User
England
62
53
User
Scotland
62
54
John Ewart
England
62
55
Tim Gatty
England
62
56
Simon
England
61
57
User
England
61
58
User
England
60
59
Ahtif Anwar
England
60
60
Nick Thomson
England
60
61
Harjan Khaira
England
60
62
User
England
60
63
Bob
England
59
64
User
England
59
65
Anastasia
England
59
66
User
England
59
67
User
England
59
68
Max Bridge
England
59
69
User
England
59
70
User
England
58
71
Marek Kurczynski
England
57
72
Andrew Koto
England
57
73
User
England
57
74
Edmund Cox
England
56
75
Jack Treanor
England
56
76
VN
Region
56
77
Chetan K
England
55
78
User
England
55
79
User
England
55
80
shanoon kadds
England
55
81
User
England
55
82
User
England
54
83
User
Region
54
84
BuzzB
Scotland
54
85
ABZX
England
54
86
tom moore
England
54
87
stephen Allison
England
53
88
MB
England
53
89
User
England
53
90
User
England
53
91
User
Wales
53
92
oliver idowu
England
53
93
aka
England
53
94
User
England
53
95
Lydima ma
England
53
96
Joe
England
52
97
User
England
52
98
User
England
52
99
User
England
52
100
User
Wales
52
101
User
England
52
102
JJJJ
England
52
103
George K
England
52
104
Zoe
England
52
105
User
England
52
106
George
England
52
107
User
Wales
52
108
George Carter
England
51
109
User
England
51
110
James Froehlich
England
51
111
User
England
51
112
User
England
51
113
User
England
50
114
zahrarajaratnam
England
50
115
User
England
50
117
User
Scotland
50
118
User
England
50
119
Sacha
England
50
120
User
England
50
121
Junior Okyere
England
50
122
User
England
49
123
Marc P
England
49
124
User
England
49
125
User
England
49
126
Gav N
England
49
127
User
England
49
128
User
England
49
129
User
England
49
130
User
Wales
49
131
Rebecca Cantrill
England
49
132
User
England
48
133
JP
England
48
134
User
Scotland
48
135
User
England
48
136
User
England
48
137
劉健聰Kenny
England
48
138
User
England
48
139
User
England
48
140
Sara
England
48
141
Calum Hughes
England
48
142
Tayip
England
48
143
Alex Hanrahan
England
48
144
Will
England
48
145
isuck@division
England
48
146
User
England
48
147
User
England
47
148
User
Scotland
47
149
Nick
England
47
150
User
England
47
151
User
England
47
152
User
Scotland
47
153
User
Scotland
47
154
User
England
47
155
User
England
47
156
User
England
47
157
User
England
47
158
Timi Arulefela
England
47
159
User
England
47
160
User
England
47
161
User
England
47
162
User
England
46
163
Brad White
England
46
164
User
England
46
165
Tony
England
46
166
George Katsou
England
46
167
User
England
46
168
User
England
46
169
User
England
46
170
User
England
45
171
User
England
45
172
User
England
45
173
Nina P
England
45
174
Jahan14
England
45
175
User
England
45
176
User
England
45
177
User
England
45
178
User
England
45
179
User
Scotland
45
180
User
England
45
181
User
England
45
182
User
England
45
183
User
England
44
184
User
England
44
185
Frankburton
England
44
186
User
England
44
187
Liliana Odjo
England
44
188
User
England
44
189
User
England
44
190
User
England
44
191
User
England
44
192
User
England
44
193
Jiahung Li
England
44
194
User
England
44
195
User
England
43
196
viggy
England
43
197
User
England
43
198
User
England
43
199
Kai Braunbeck
England
43
200
User
England
43
201
User
England
43
202
Dan Havins
England
43
203
User
England
43
204
Yousef
England
43
205
User
England
43
206
User
England
43
207
E.P. Thompson
England
42
208
User
England
42
209
User
England
42
210
Achintya Singh
England
42
211
User
England
42
212
wilma6993
England
42
213
User
England
42
214
User
England
42
215
User
England
42
216
Bruce Boutell
England
42
217
User
England
42
218
User
England
42
219
User
Wales
42
220
User
England
42
221
User
England
42
222
User
England
42
223
User
England
42
224
User
England
41
225
User
England
41
226
Sa
England
41
227
User
England
41
228
User
England
41
229
User
England
41
231
User
England
41
232
User
England
41
233
User
England
41
234
User
Wales
41
235
User
England
41
236
User
England
41
237
User
England
41
238
User
England
41
239
User
England
41
240
User
England
41
241
User
England
41
242
User
Isle of Man
41
243
User
England
41
244
User
England
41
245
User
England
41
246
User
England
40
247
Rob
England
40
248
User
England
40
249
User
England
40
250
User
England
40
251
User
England
40
252
Resources Stuff
England
40
253
User
England
40
254
User
England
40
255
User
England
40
256
User
England
40
257
User
Scotland
40
258
User
England
40
259
Chris
England
40
260
Louis Goulding
England
40
261
User
England
40
262
ifu05444
England
40
263
A Carter
England
39
264
User
England
39
265
User
England
39
266
User
England
39
267
Yellow Ninja
England
39
268
User
England
39
269
Angus Simpson
England
39
270
User
England
39
271
User
England
39
272
Ulrich Hornheimer
England
39
273
User
Wales
39
274
User
England
39
275
User
England
39
276
User
England
39
277
User
England
39
278
User
England
39
279
User
England
39
280
User
England
39
281
User
England
39
282
User
England
38
283
User
England
38
284
User
England
38
285
George Hall
England
38
286
Abs Arosi
England
38
287
Ella Barnes
England
38
288
Aliya boiiii get off meh account mate
England
38
289
Richard Clouter
Scotland
38
290
User
England
38
291
User
England
38
292
Ali Khan
England
38
293
Epsilon Delta
England
38
294
Jacob Fisher
England
38
295
User
England
38
296
User
England
38
297
User
England
38
298
User
England
38
299
User
England
38
300
Abbie Robinson
England
38
301
Zana Osmani
England
38
302
User
England
38
303
User
England
37
304
User
England
37
305
Benjamin Irwin
England
37
306
User
England
37
307
User
England
37
308
User
England
37
309
User
England
37
310
User
England
37
311
User
England
37
312
User
England
37
313
User
England
37
314
User
England
37
315
User
Scotland
37
316
User
England
37
317
Joseph Hickie
England
37
318
User
England
37
319
Salman Hussain
England
37
320
User
England
37
321
User
England
37
322
P McC
England
37
323
Afnan Sayam
England
36
324
User
England
36
325
Ernie T
England
36
326
User
England
36
327
User
England
36
328
User
England
36
329
User
England
36
330
Stephen Mellor
England
36
331
User
England
36
332
Yo jam
England
36
333
Dasha P.
England
36
334
bexgravell
England
36
335
Morgan
England
36
336
Time Zone Gaming
England
36
337
User
England
36
338
User
England
36
339
User
Scotland
36
340
User
England
36
341
User
England
35
342
User
England
35
343
User
England
35
344
Tom Levy
England
35
345
User
England
35
346
User
England
35
347
User
England
35
348
User
England
35
349
Hanh
England
35
350
amir jarada
England
35
351
User
England
35
352
User
England
35
353
User
England
35
354
User
England
35
355
User
Wales
35
356
User
England
35
357
User
England
35
358
Tahmid Rahman
England
35
359
User
England
34
360
User
England
34
361
User
England
34
362
User
Scotland
34
363
User
England
34
364
User
England
34
365
User
Scotland
34
366
User
England
34
367
User
England
34
368
Alex Bor
England
34
369
User
England
34
370
User
Scotland
34
371
User
England
34
372
Freddy Fan
England
34
373
User
England
34
374
User
England
34
375
Amy Szarvas
England
34
376
User
England
34
377
HOE
England
34
378
User
England
34
379
User
England
34
380
anonymous anonymous
England
34
381
L T
England
34
382
Reuben Mason
England
34
384
User
England
33
385
User
England
33
386
User
England
33
387
User
England
33
388
User
England
33
389
Ben Alfert
England
33
390
y08g09
England
33
391
Sophie Payne
England
33
392
Elect Akalonu
England
33
393
User
England
33
394
User
England
33
395
Emmanuel Alen
England
33
396
Ratatouille
England
33
397
User
England
33
398
User
England
33
399
User
England
33
400
User
England
33
401
User
England
33
402
shaz khan
England
33
403
Charles Siu
England
33
404
User
England
33
405
User
England
33
406
User
England
33
407
User
England
33
408
User
England
33
409
User
England
32
410
User
England
32
411
User
England
32
412
Toby
England
32
413
User
England
32
414
User
England
32
415
User
England
32
416
User
England
32
417
User
Wales
32
418
andrew
England
32
419
User
England
32
420
User
England
32
421
User
England
32
422
User
England
32
423
Paul Joseph
England
32
424
买了否冷
England
32
425
Davide Uccello
Scotland
32
426
User
England
32
427
User
England
32
428
User
Scotland
32
429
User
England
32
430
User
Scotland
32
431
Rachel Stephanie van den Broek
England
32
432
User
England
32
433
User
England
32
434
User
England
32
435
User
England
32
436
Ewan Marshalsay
Region
32
437
User
England
32
438
User
England
32
439
User
Scotland
32
440
User
England
32
441
User
England
32
442
User
England
31
443
User
Scotland
31
444
User
England
31
445
User
England
31
446
User
England
31
447
User
England
31
448
User
England
31
449
User
England
31
450
User
England
31
451
User
England
31
452
User
England
31
453
User
England
31
454
User
England
31
455
User
England
31
456
clive
England
31
457
User
England
31
458
gautham ravisankar
England
31
459
Mari Gravell
England
31
460
Tobbles
England
31
461
User
Scotland
31
462
Abi
Wales
31
463
User
England
31
464
User
England
30
465
User
England
30
466
User
England
30
467
User
England
30
468
Anthony Johnson
England
30
469
User
England
30
470
User
England
30
471
User
Scotland
30
472
Aaron Bowers
Scotland
30
473
User
England
30
474
User
England
30
475
User
England
30
476
Georgia Brown
England
30
477
User
Scotland
30
478
User
England
30
479
User
England
30
480
User
England
30
481
User
England
30
482
Mike Diplock
England
30
483
User
England
30
484
User
England
30
485
User
England
30
486
User
England
30
487
User
England
30
488
User
England
30
489
User
England
30
490
User
England
30
491
User
England
30
492
User
England
30
493
benita stipp
England
30
494
User
England
30
495
winky
England
30
496
User
England
30
497
User
England
30
498
User
England
29
499
User
England
29
500
User
England
29
501
User
England
29
502
User
England
29
503
User
England
29
504
Josh Paul
England
29
505
User
England
29
506
Suyash Poshakwale
England
29
507
User
England
29
508
User
England
29
509
User
England
29
510
User
England
29
511
User
England
29
512
User
England
29
513
Mykhailo Tkach
England
29
514
vv
England
29
515
User
England
29
516
User
England
29
517
User
England
29
518
User
Scotland
29
519
User
England
29
520
User
England
29
521
User
England
29
522
User
England
29
523
User
England
29
524
User
England
29
525
User
England
29
526
User
England
29
527
User
England
29
528
Prof Lishkov
England
29
529
User
England
29
530
User
England
29
531
User
England
29
532
Kathy Hulme
England
29
533
User
England
28
534
User
England
28
535
User
England
28
536
User
England
28
537
User
England
28
538
User
England
28
539
Asvigaa Ganesh
England
28
540
User
England
28
541
User
England
28
542
User
England
28
543
User
England
28
544
User
England
28
545
Box
England
28
546
User
England
28
547
User
England
28
548
Jen Furmston
England
28
549
User
England
28
550
User
England
28
551
User
England
28
552
User
England
28
553
User
England
28
554
User
England
28
555
User
England
28
556
User
England
28
557
User
England
28
558
User
England
28
559
User
England
28
560
User
England
28
561
Matthew
England
28
562
James Morris
England
28
563
User
England
28
564
User
England
28
565
User
England
28
566
User
England
28
567
User
Scotland
28
568
User
Scotland
28
569
Srish
England
28
570
User
England
28
571
User
England
28
572
User
England
28
573
User
Scotland
28
574
User
England
27
575
User
England
27
576
User
England
27
578
User
England
27
579
DC
England
27
580
User
Region
27
581
User
England
27
582
User
Scotland
27
583
User
England
27
584
User
England
27
585
User
England
27
586
User
England
27
587
User
England
27
588
User
England
27
589
User
England
27
590
User
England
27
591
User
England
27
592
User
England
27
593
edward stubbs
England
27
594
User
England
27
595
User
England
27
596
Nikolay Momchev
Scotland
27
597
User
England
27
598
User
England
27
599
Iona Ffrench-Adam
England
27
600
User
England
27
601
User
England
27
602
User
England
27
603
User
England
27
604
User
England
27
605
User
England
27
606
User
England
27
607
User
England
27
608
Ricky Green
England
27
609
User
England
27
610
Anisa Sharmin
England
27
611
User
England
27
612
User
England
27
613
User
England
27
614
User
England
27
615
User
England
27
616
Brian Osarchos
England
26
617
mb8993
England
26
618
User
England
26
619
User
England
26
620
User
England
26
621
User
England
26
622
Pak
England
26
623
User
England
26
624
User
England
26
625
User
England
26
626
User
England
26
627
User
England
26
628
User
England
26
629
Kush Patel
England
26
630
User
England
26
631
User
England
26
632
User
England
26
633
User
England
26
634
User
England
26
635
Radek
England
26
636
kinu
England
26
637
User
England
26
638
User
England
26
639
User
England
26
640
User
England
26
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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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