Where do I find a 99x99 multiplication table?
Here’s a spreadsheet with that data (tab-separated values). If you prefer another format or need any other tools, let me know. 
Edit: the files were moved to the free worksheets page.
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Thank you John! This saved me a lot of time.
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What’s your plan with those?
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Memorize 
I read in Alberto Coto’s book Entrenamiento Mental that mental calculus athletes memorized the multiplication table 99 x 99 to use 2 numbers at a time by the cross multiplication method.
But I have no plans to memorize this table this month. I am involved in building the shadow system. I am struggling to finish my shadow system this week. Ah, thanks for helping me understand the shadow system
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Big project… might wanna start with the squares 11^2 - 99^2 which will already allow you to do the 2-digit criss-cross approach you’ve mentioned, albeit via difference of squares. On the other hand, that’s a lot of impact for just 90 numbers. You can then start adding the rest of them as needed.
I’ve just done exactly that (memorized the squares). I’ll probably write a post about the method I’ve used once I got a bit of free time…
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By request, I’ve just added a file that lists them like this:
2 × 2 = 4
2 × 3 = 6
2 × 4 = 8
2 × 5 = 10
2 × 6 = 12
2 × 7 = 14
2 × 8 = 16
2 × 9 = 18
...
99 × 90 = 8910
99 × 91 = 9009
99 × 92 = 9108
99 × 93 = 9207
99 × 94 = 9306
99 × 95 = 9405
99 × 96 = 9504
99 × 97 = 9603
99 × 98 = 9702
99 × 99 = 9801
See my comment above to download the entire file.
The files only show 2-99, because multiplying by 0 and 1 don’t require calculation or memorization.
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If you’re looking for a 99x99 multiplication table, there are many online resources available that you can use.
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Um, I realise this isn’t the point, but when you say memorise the squares do you mean all of them, or just the ones that are hard to do by completing the square? Like, 99x99 is (99 +1)(99 -1) is (100*98)+1 (I find the 30s and the 70s hard⁰, but certainly easier than a direct memorisation… )
EDIT - ah, I have followed some links and I understand that you used to do calculations like this and now cache for speed. That’s cool. Seperate question - the sentence “already allow you to do the 2-digit criss-cross approach you’ve mentioned, albeit via difference of squares” confuses and fascinates me - where can I learn more?
⁰ So much so I cheat a little when I perform this and force a different number
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Multiplying by difference of squares. This technique applies when the difference between the two numbers is even and exploits the algebraic relation
(a+b)(a-b) = a2-b2
eg 74*76 = (75+1)(75-1) = 752 -12 = 5625-1
If you know the squares (or can rapidly figure them) this trick can be very useful.
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ooooh. That’s something I’ve never seen before. Thank you.
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What do you mean by this 11^2 - 99^2?
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what does he mean by memorising 11^2 - 99^2?
If you wouldn’t mind me to answer to that question,
Here is why @bjoern.gumboldt said that.
If you memorize 0 to 99 numbers squares it will help you in multiplying close numbers.
for example :
84 × 88 (now, I am assuming you did your task of memorizing squares)
For this you have to think of the middle digit square and subtract half of difference square.
86² - 2² = 7396 - 4 = 7392
To put it more simply, just remember to think of the middle digit square and subtract every time 4. If the difference is 4.
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Thanks, but what if you have 46 X 57, how are you going to do this? Is the difference of squares the best method, I have good memory for numbers already, I need to get good at mental amths.
You can use the Diff of squares to multiply 46*56 and add 46 to the result. But probably better to use the Anker method in this case. Diff of sqs works best when the difference is even.
Anker (Dutch for Anchor):
46x57 = (50-4)x(50+7) – anker chosen as 50
= 50x(46+7) + (-4x7)
= 2650 -28
= 2622
Both the Anker and Diff of Sqs are useful when the numbers are close or can be made close (divide one multiplier by 2, for example). In such cases, these methods can be very quick if one is well practised and spots the opportunity without wasting time. Otherwise it’s the criss cross method.
for difference of even numbers I already told you the way.
(Middle digit square) - (Half of difference)²
Now let’s come to the topic.
If the difference is odd
• when the difference is 3
18 × 21
(Smaller digit + 1)² + (smaller digit - 1²)
(18 + 1)² + (18-1)
(19)² + (17)
361 + 17 => 378
• When the difference is 5
18 × 23
(Smaller digit + 2)² + (Smaller digit - 2²)
(18 + 2)² + (18 - 4)
400 + 14 => 414
• When the difference is 7
22 × 29
(Smaller digit + 3)² + (Smaller digit - 3²)
(22 + 3)² + (22 - 9)
625 + 13 => 638
• When the difference is 9
72 × 81
(Smaller digit + 4)² + (Smaller digit - 4²)
(76)² + (56)
5776 + 56 => 5832
I guess it’s more than sufficient to clear your doubts.
Well, I use this only when the difference is 3, 5, 7
I don’t go for this if the difference is larger.
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