comenius math and science studio. funny math how is it possible?
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Comenius Comenius Math and Science StudioMath and Science Studio
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Funny mathFunny math
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How is it possible?
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ResolutionResolution
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ResolutionResolution
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Magic numberMagic number
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Think of three number digit
The first digit must be two digits different from the third one
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write the number in inverted form
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Now you get two numbers
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subtract the smaller number of the larger one
for example 782 – 287 = 495
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now write the result in inverted form and add up two numbers
In this situation 495 + 594 = . . .
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the result is number
1089
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is this result just a coincidence?
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You probably think that the outcome depends on the initial numbers
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But it doesn´t!
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the result will always be equal to 1089
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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:
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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
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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.
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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 ?
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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
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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
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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
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Geometric shapes by a single line
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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.
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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
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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
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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
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Funny mathFunny math
Find x !Find x !