1. Comenius Math and Science Studio

2. Funny math

3. How is it possible?

4. Resolution

5. Resolution

6. Magic number

7. Think of three number digit The first digit must be two digits different from the third one

8. write the number in inverted form

9. Now you get two numbers

10. subtract the smaller number of the larger one for example 782 – 287 = 495

11. now write the result in inverted form and add up two numbers In this situation 495 + 594 =...

12. the result is number 1089

13. is this result just a coincidence?

14. You probably think that the outcome depends on the initial numbers

15. But it doesn´t!

16. the result will always be equal to 1089

17. 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:

18. 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

19. 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.

20. 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 ?

21. 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

22. 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

23. 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

24. Geometric shapes by a single line

25. 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.

26. 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

27. 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

28. 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

29. Funny math Find x !