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Comenius
Math and Science Studio
Funny math
How is it possible?
Resolution
Resolution
Magic 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
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

Geometric shapes by a single
line
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 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
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 math
Find x !