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Mathematics can be quite interesting.

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H.Krishnamurthy

Active member
Hello Friends , Recently I saw a puzzle in a book by a russian author.
It starts like this.
9-15= 4-10
add 25/4 ( 5/2 whole square )on either side.
9-15+25/4= 4-10+25/4
means
3 Square - 2x 3 x 5/2 + 5/2 Square = 2 Square - 2 x 2 x 5/2 + 5/2 square.
means (3-5/2 ) whole square = ( 2 - 5/2 ) whole square.
Take square root on both side means
3 - 5/2 = 2 - 5/2
Cancel 5/2 on either side
means
3 = 2 ???????
how is this possible.
Shall mail solution in my next posting.
H.Krishnamurthy..
 

sravna

Well-known member
Hello Friends , Recently I saw a puzzle in a book by a russian author.
It starts like this.
9-15= 4-10
add 25/4 ( 5/2 whole square )on either side.
9-15+25/4= 4-10+25/4
means
3 Square - 2x 3 x 5/2 + 5/2 Square = 2 Square - 2 x 2 x 5/2 + 5/2 square.
means (3-5/2 ) whole square = ( 2 - 5/2 ) whole square.
Take square root on both side means
3 - 5/2 = 2 - 5/2
Cancel 5/2 on either side
means
3 = 2 ???????
how is this possible.
Shall mail solution in my next posting.
H.Krishnamurthy..

Can others post their solution?
 

CLN

Active member
It is a simple but famous fallacy, some times used by maths teachers to arouse the interest of students in the subject. As Shri HK wants to post the solution himself I do not want to spoil his enthusiasm. Any way I will give a subtle hint to those who wish to try to solve the puzzle themselves. "Beware of square roots!"
 
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CLN

Active member
Sure Kunjuppuji, I do believe you! :)

As a token of my belief I give below another famous and not very difficult puzzle below:

Make an eight-digit number using two 1's, two 2's, two 3's and two 4's such that in the number thus formed, there lies just one digit between the two 1's, two digits between the two 2's, three digits between the two 3's and four digits between the two 4's.

Believe me, it is NOT really so very difficult as it sounds! Any one can try and post the solution!
 

Visalakshi Ramani

Well-known member
I can also give a hint to the original problem!

Square root of (a square) can be (+a) or (-a)!

Apply this rule and solve the puzzle in a second!
 

CLN

Active member
Yes, there are two - but just two solutions. In fact, if you look closely at the two solutions, the digits are just in reverse order from one to another. By the way, congratulations to both of you!
 

CLN

Active member
Madam VR, for the poser of Shri HK, yours is not a hint, but part of the solution itself!

Now I feel tempted to post another puzzle here (perhaps at the risk of incurring the wrath of some members who may not feel all that kindly towards the fascinating subject of Mathematics! :) ;))

What is so special about the number 2519 ?
 

zebra16

Well-known member
Folks,

While you are raking your brains to find a solution, here is a bit of relief:

Last week I purchased a burger at Burger King for
$1.58. The counter girl took my $2 and I was digging
for my change when I pulled 8 cents from my pocket and
gave it to her. She stood there , holding the nickel
and 3 pennies , while looking at the screen on her
register.

I sensed her discomfort and tried to tell
her to just give me two quarters , but she hailed the
manager for help. While he tried to explain the
transaction to her, she stood there and cried.

Why do I tell you this?

Because
of the evolution in teaching math since the
1950s:

1. Teaching Math In 1950s

A logger sells a truckload of lumber for $100. His
cost of production is 4/5 of the price. What is his
profit ?

2. Teaching Math In 1960s

A logger sells a truckload of lumber for $100. His
cost of production is 4/5 of the price , or $80. What
is his profit?

3. Teaching Math In 1970s

A logger sells a truckload of lumber for $100. His
cost of production is $80. Did he make a profit?

4. Teaching Math In 1980s
A logger sells a truckload of lumber for $100. His
cost of production is $80 and his profit is $20. Your
assignment: Underline the number 20.

5. Teaching Math In 1990s
A logger cuts down a beautiful forest because he is
selfish and inconsiderate and cares nothing for the
habitat of animals or the preservation of our
woodlands. He does this so he can make a profit of
$20. What do you think of this way of making a living?

Topic for class participation after answering the
question: How did the birds and squirrels feel as the
logger cut down their homes? (There are no wrong
answers , and if you feel like crying , it's ok.

6. Teaching Math In 2009

Un hachero vende una carretada de maderapara $100. El
costo de la producciones es $80. Cuanto dinero ha
hecho?
--- forwarded email received about 3 years ago - is my claim correct??

Regards,

narayan
 
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CLN

Active member
Brilliant Mr. narayan, at your telling illustration of the "evolution"(???) of Mathematics Teaching from 1950 to 2009 (in US), particularly when the problem in arithmetic gave way to an ecology and environment issue! No wonder the girl at the counter was flabbergasted, not knowing what to do with your 8 cents!
 

sravna

Well-known member
Madam VR, for the poser of Shri HK, yours is not a hint, but part of the solution itself!

Now I feel tempted to post another puzzle here (perhaps at the risk of incurring the wrath of some members who may not feel all that kindly towards the fascinating subject of Mathematics! :) ;))

What is so special about the number 2519 ?

The whole number can be got this way: (251 x 9) + (251+9)
The last three digits can be got this way: (51 x 9) + (51+9)
The last two digits can be got this way : (1 x 9) + (1 +9)
 

zebra16

Well-known member
The whole number can be got this way: (251 x 9) + (251+9)
The last three digits can be got this way: (51 x 9) + (51+9)
The last two digits can be got this way : (1 x 9) + (1 +9)

great sravana !!!!!!!!!!!!

Regards,

narayan
 

Visalakshi Ramani

Well-known member
It WORKS for the number 3459 but not for 2719!

So I a sure there is a limiting value above which this may work for many

numbers ending in 9-even if not for all the numbers ending in 9!

Or it may work for numbers ending in 59!

Needs further investigation!
 

Visalakshi Ramani

Well-known member
YES FOLKS!

It works for numbers ending in 59!

I tried with 7659 and 8459!

Both worked. Is the magic of the last two digits 59! WOW great fun!

So 2519 is not so special after all it is the 59 at the end that makes the

numbers special!
 

Visalakshi Ramani

Well-known member
It works for three digit numbers also ending in 59 . I tried 759 and 359.

Must try with 5 digit numbers later. Now the kitchen chores call me!

Already running behind schedule! :clock:
 
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