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Discover intriguing mathematical phenomena like the 1089 mystery, age puzzles, and geometric shape drawings with a single line. Explore the world of funny math tricks and mind-bending puzzles here!
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Think of three number digit The first digit must be two digits different from the third one
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
You probably think that the outcome depends on the initial numbers
Explanation • We first chose the three digit number • We wrote the number in reverse order of numbers • We 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
Lamps • The 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.
Lamps • The 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 - explanation • A multiple of three numbers must be 36 • 1*1*36=36 • 1*2*18=36 • 1*3*12=36 • 1*4*9=36 • 1*6*6=36 • 2*2*9=36 • 2*6*3=36 • 3*3*4=36
Lamps - explanation • the sum of three numbers must give the same results • 1+1+36=38 • 1+2+18=21 • 1+3+12=16 • 1+4+9=14 • 1+6+6=13 • 2+2+9=13 • 2+6+3=11 • 3+3+4=10
Lamps - explanation • you are getting two equal answers • 2+2+9=13 • the second result is correct, because the oldest brother is called Charles • number 13 is a number of the lamps in the street
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. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Solution 1. -two knots with an odd calculusof lines (right and left down), rest knotseven => can draw by a single line 2.-beginning in one of the odd nodes=> right or left down - all knots is even=> can drawby a single line and beginning any 3. - two knots with an odd calculus of lines(leftdown and on high), rest knotseven => can draw by a single line - beginning in one of the odd nodes => left on high or down 4. - all knots is even => can drawby a single line and beginning any 5. - all knots is even => can drawby a single line and beginning any
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 possiblenumber 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=> wecan 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
Funnymath Find x !
