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How is it possible?

ResolutionResolution

ResolutionResolution

Magic numberMagic number

Think of three number digit

The first digit must be two digits different from the third one

write the number in inverted form

Now you get two numbers

subtract the smaller number of the larger one

for example 782 – 287 = 495

now write the result in inverted form and add up two numbers

In this situation 495 + 594 = . . .

the result is number

1089

is this result just a coincidence?

You probably think that the outcome depends on the initial numbers

But it doesn´t!

the result will always be equal to 1089

ExplanationExplanation

We first chose the three digit numberWe wrote the number in reverse order of numbersWe subtracted the lower number from the larger Decimal notation of the larger number:

Decimal notation of the lower number:

Subtraction:

a and c are integral numbers and so we always get multiples of 99

The triple-digit multiples of the number 99 are 198, 297, 396, 495, 594, 693, 792, 891

We see immediately that the sum of the first and third number is always 9

So we get from the first numbers 900, 9 from the third numbers and 2*90 from middle numbers: 900 + 180 + 9 = 1089

LampsLampsThe teacher introduced a challenging task

to his student:I have three sons.When you multiple their ages, the result is

36. The sum of their ages is equal to the

number of lamps in this street.

LampsLampsThe pupil thought about it and said : This

is not enough for me, I can not say exactly how old they are.

The teacher answered. Well, the oldest son is called Charles

How old are the sons ?

Lamps - explanationLamps - explanationA multiple of three numbers must be 361*1*36=361*2*18=361*3*12=361*4*9=361*6*6=362*2*9=362*6*3=363*3*4=36

Lamps - explanationLamps - explanationthe sum of three numbers must give the same

results1+1+36=381+2+18=211+3+12=161+4+9=141+6+6=132+2+9=132+6+3=113+3+4=10

Lamps - explanationLamps - explanationyou are getting two equal answers2+2+9=13the second result is correct, because the oldest

brother is called Charlesnumber 13 is a number of the lamps in the street

Geometric shapes by a single line

1. 2. 3. 4. 5.

6. 7. 8. 9.

10. 11. 12. 13.

Find which shapes can be drawn by a single line and give reasons why . The shapes which can be drawn by a single line, determine how to start, so that drawing could be done and give reasons.

1. -two knots with an odd calculus of lines (right and left down), rest knots even => can draw

by a single line

2. -beginning in one of the odd nodes => right or left down

- all knots is even=> can draw by a single line and beginning any

3. - two knots with an odd calculus of lines(left down and on high), rest knots even => can draw

by a single line

- beginning in one of the odd nodes => left on high or down

4. - all knots is even => can draw by a single line and beginning any

5. - all knots is even => can draw by a single line and beginning any

Solution

6. -two knots with an odd number of lines (down and up), the rest of knots even => can draw a single line

- begin with one of the odd nodes => up and down

7. -four odd knots (the maximum possible number of odd knots is two, in one we start drawing and we finish in the other)=> don´t by a single lin

8. -all knots are even=> we can draw a single line and begin on any of them

9. -all knots are even => we can draw a single line and begin on any of them

10. - four an odd knots (the maximum possible calculus odd knots is two, in one we will start charting and in other we will finish)=> not draw by a single line

11. - two knots with an odd calculus of lines (right and left on high), rest knots even => can draw by a single line

- beginning in one of the odd nodes => right or left on high

12. - two knots with an odd calculus of lines (down or on high), rest knots even => can draw by a single line - beginning in one of the odd nodes => down or on high

13. -all knots is even=> can draw by a single line and beginning any

Funny mathFunny math

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