The digits are the ones used in decimal coding ... .
Eliminating multiples of 3 and 9 may help in checking .
Evenodd check is to be added. It works well for the last digit.
Orderly work prevents this error but we do not always work orderly.
Dogs are no sheep and count also legs in case of decision difficulties.
Though bacgrounds differ the triangles are the same, but that is not what the fig. transmits.
Number are abstraction, each is unidentifiable. Object are mostly identifiable.
The first form of mental calculations is based upon digital expansion, use of any trick is not made, the number 387 is thought as 3x100 +
8x10 + 7
The second form consists of using a formula we have learned before. This sum is 500x1001 = 500x1000 + 500
Here we make use of the fact that 1 + 999 = 1 000
Here we have to reorder: 1282 + 1718 + 765 + 535 + 1453 + 147 + 351 = 3000 + 1300 + 1600 + 100 + 251 =
Here we can make use of something we already know. 1776 is the year of Decleration of Independence and we have heard of 235th anniversary of
DoI in 2011.
Here we can reorder and make use of something we already know: ...= 12700 + 12800 + 1.14x12750 = 3.14 x 12750 is something around 40000 (we
know the diameter and the perimeter of the Earth)



YEHUDI MENUHIN SHOULD HAVE SAID :"IF I DO NOT PLAY FOR A DAY, I FEEL; IF I DO NOT PLAY FOR A WEEK, MY AUDIENCE FEELS ..."
A CONVERSATION BETWEEN TWO DIPLOMATS OF TWO DIFFERENT COUNTRIES:
 WHAT IS THE DIFFERENCE BETWEEN YOUR CITIZENS AND SPENDTHRIFTS ?
 WELL, NOT A POLITE QUESTION, MAY I TAKE YOUR ANSWER ?
 SURE, ONE SPENDS THAT EXIST; THE OTHERS NON EXISTING ...
AFTER A WHILE THE OTHER DIPLOMAT ASKS THE FIRST AND ...
 WHAT IS THE DIFFERENCE BETWEEN YOUR CITIZENS AND SPENDTHRIFTS ?
 WELL, I CAN NOT SAY EXACTLY, MAY I TAKE YOUR ANSWER ?
 SURE, ONE SPENDS THAT EXIST; THE OTHERS TO MAKE EVERYTHING, THE WHOLE WORLD, DISTINCT ...
Addition of two odd numbers gives an even, I can not be correct .
1238  449 = 1249  11  449 = 800  11 = 789 and III similarly .
... because a ten is transferred as a one .
Checking the multiples of 9 eliminated digit sums we see I is incorrect and only one of the choices contains it .
Considering Bx10 + A = Ax10 + B  9 we find 10x(BA) = (BA)  9 i.e. B  A = 1.
Red lines correspond respectively to 10 , 6 and 4 billions.
Accept that the average human life has been around 50 years and there lived an average population of :
Between 10000  5000 BC about 50 millions.
Between 5000 BC  0 about 200 millions.
Between 0 and 1900 AC about 400 millions and
Between 1900  2000 AC about 3 billions.
Based on our assupmtions, between 100005000 BC there lived 5 000 million /50 x 50 = 5 billion human on Earth. And the others are resectively
20 billion, 15.200 and 6 billion .
Use the followings :
Addition of an even and an odd numbers gives an odd number .
If the digit sum of the summands is a multiple of 3, the digit sum of the sum is also ...
Remember the def. of factorial and make use of it .
This is the feedback!