Memoriad Additions: how to solve it quickly? Part 2

Here is how I do column addition.

First 1 column at a time.

Next post I will do columns with 2 digits.

Let’s take Benjamins example:

In his example we see a matrix with 10 rows.
What I do is first add all numbers that add up to a round number (i.e. 10, 20, etc.).

Since we are doing right to left, let’s stick with that.

Most right column exist of the digits: 8 2 4 3 7 9 9 5 6.
In my mind I go over the digits and take out the digits that add up to 10 (or 20):

1: 8 2
2: 3 7 (skipping 4 for later)
3: 9 5 6 (while glancing over the digits I recognize 6+5 = 11. So almost immediately I see that the last 3 digits add up to 20).

My sub total is 40.
Left to do: 4 + 9 = 13

Total for first column is 53.
Write down 3 and carry 5.

The second column starts with 5, so take the carry and add the 5 to be the first 10:
1: 5 5
2: 6 4 (skip the 8 for the next step)
3: 8 2 (again we skip the 4)
4: 2 8

Sub total: 40

Left to do: 8 + 8 = 16

Total is 56. Write down 6. Carry 5.

Third row - including the carry - is: 5 9 8 8 …

It might not be immediately obvious that this adds up to a round number. However 5 + 9 = 14 and the complement of 8 is 2. Thus adding each 8 subtracts 2 from the last digit. So adding 2 8’s remove ‘4’ from the subtotal of 14.
In short 5+9+8+8 = 30.

Same with next 4: 8+7 = 15 and 6+9 = 15, so the next 4 digits add up to 30.

Subtotal for the first 7 digits is 60. left to do is adding ‘9+0+8’.
I hope you see immediately that this is 17.

Total is 77.

etc.

In short; I glance over the 10 digits in a column and remove the digits that add up to a round number.
I realize that this has a risk that you forget to add a digit.
However; for me, this goes pretty fast.

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Like I promised, let’s now do 2 digits per column.
Same calculation as the previous post.

I hope you immediately see that 58 + 62 = 120.
If not, take 58, add the 2 from ‘62’ to get 60 and then add 60. 60+60 = 120.

Next step 120 + 84. I immediately see 204.
If not; Add 80 to 120 first to get 200 and then add the 4: 204

Now make a side step and add the 43+27 = 70 first.
Since 70 ‘slides’ into 204, we get 274.

Now add 20: 294.

We get to the 89. Either see the 300’s complement of 294 = 6 or the 100’s complement of 89 = 11.
I see the 6 quicker than the 11 (don’t know why), so in my mind I see 300 and 83 = 383

Add 9: 392

Add 85. Either take complement 8 (of 392) or 15 (of 85). I take 8. So make a side step of subtracting 8 from 85. Subtract 5 first => 80. 3 left to do => 77.

(btw, this is where experience with the soroban makes this easier. Think about how the beads move if you do this. In your mind put 85 on the soroban. Then subtract 8 :slight_smile: )

Result 477.

Add 86. Now the complement of 14 comes up quicker than 23.
77-14 = 63.

Total = 563.


Of course if you combine this with finger counting, you can either put the subtotals on your fingers and if you type the numbers with your right hand, put the carry on your left.

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