Number Puzzle #161

If

2-1=3

4-4=0

8-5=40

10-10=???

Check your answer:-

here a-b=axa+(a/2)x(a/2)-axb

2-1=2×2+(2/2)x(2/2)-2×1=3

8-5=8×8+(8/2)x(8/2)-8×5=40

4-4=4×4+(4/2)x(4/2)-4×4=4

thus

10-10=10×10+(10/2)x(10/2)-10×10=25

Harvey Lerman says

a-b=???

axa+(a/2)x(a/2)-axb=answer

10-10=10×10+(10/2)x(10/2)-10×10=25

2-1=2×2+(2/2)x(2/2)-2×1=3

8-5=8×8+(8/2)x(8/2)-8×5=40

4-4=4×4+(4/2)x(4/2)-4×4=4

Rajeev says

in Question, 4-4 = 0, whereas in your explanation, 4-4 = 4 . Does not make sense

Harvey Lerman says

Guess you caught me in a “typo”.

It should be 4-4=4.

I apologize to all!

Harvey Lerman says

Answer to puzzle:

10-10=25

Format of puzzle:

a-b=?

Equation:

a*+(a/2)*-axb [where * means square, x=mult]

Could be stated as (5a*/4-axb)

So 10-10:

10×10+[10/2]x[10/2]-10×10=

100+5×5-100=25

extra

8-5:

8×8+4×4-8×5=64+16-40=40

Sat Battoo says

Sorry Harvey, I’m not getting it.

1) How did you come up with the equation?

2) When you say a* + (a/2)* – axb, could be stated as (5a* / 4-axb), these two are not equal.

3) a* + (a/2)* – axb works for the first part, 2-1=3 and also 8-5=40 but doesn’t work for 4-4=0 because 4-4 works out to be -4.

4) The (5a* / 4-axb) formula doesn’t work for any of them.

Please advise.

Harvey Lerman says

It’s confusing because I can’t type subscripts, etc.

1. (half of a)-squared can be written as (a/2)-squared or a-squared/2-squared which is a-squared/4.

2. also a-squared can be written as (4 a-squared)/4

adding these together gives (5a-squared)/4

So they are the same and either way you put it all together gives the correct answers to all the examples I gave, including the equation:

10-10=25.

4-4=(16+4)-16=4

10-10=(100+25)-100=25

Harvey Lerman says

Hope the “a-squared” doesn’t get confused with “-” used as “minus”.

I should have used maybe “a_squared”

gaurav mane says

ans 10-10/10/10=1

Harvey Lerman says

Let me know when you all give up and I’ll tell you the correct answer. Or I can give you other examples: 6-3=27 also 4-2=12

avinash Chinna says

could you tell what’s the answer is?

Deepti Singhal says

answer is 1

Pruthiraj Swain says

Hi, Could you pls tell me the logic behind it?? How you got 1 as answer ?? Pls help me

Deepti Singhal says

Hi the logic is

2-1=3 ( actually its addition)

4-4=0 (actually its subtraction)

8-5=40 (actually it multiplication)

since all the arithmetic operations are used only pending is division

hence 10-10=1 (actually it is 10/10=1)

i hope you got it!!

Happy Puzzling ðŸ˜€

Swati says

How

Dhvani says

10-10=1