Math Fun

-1. When I add 2 times my age 2 years from now to 3 times my age 3 years from now, I get 6 times my current age. How old will I be 5 years from now?"

2. Arrange the numbers 1-32 in a circle so that any two adjacent numbers sum to a square number. For Example : 1-8-28 ... ( 1+8=sq(3) and 8+28=sq(6) )

-3. Three circles are bound together by a rubber band as shown in the figure. Assume the diameter of each circle is 10 cm; then how long is the rubber band if it is stretched as shown?



-4. Mick and John were in a 100 meter race. When Mick crossed the finish line, John was only at the 90 meter mark. Mick suggested they run another race. This time, Mick would start ten meters behind the starting line. All other things being equal, will John win, lose, or will it be a tie in the second race?

MICK:@m............100..............>t
JOHN:@j...........90..........>t
100/m = 90/j : j = 9m / 10

@m.................110........................>110/m
***10***@j...............100..............>100/j = 100/(9m/10)

110/m - 100/(9m/10)
= 110/m - 1000/(9m)
= 990/(9m) - 1000/(9m)
= -10/(9m) : so poor John loses again !!

Right you are, Denis!

3.


Line segments, AB, CD, and EF are all 10cm in length.
Arc BC spans 120deg of the circle.
Circumference of the circle is 10pi so

Length of arc BC is (120/360)10pi = (10/3)pi

Length of the rubber band = 10+10+10+3(10/3)pi = 30+10pi

Perfectly done!

1. Let x be your current age.
2(x+2) + 3(x+3) = 6x
5x + 13 = 6x
13 = x
Your current age is 13, 5 years from now your age will be 18

1. You will be 18 in 5 years time, being 13 now - (2 x 15) + (3 x 16) = 78 = 6 x 13

Probably feels like only yesterday!

More mathematical integrity in manxman's answer - mine was trial and error.

Both correct!

Morning walk analysis:
- arranging in straight line ok, but 1st + last = a square
- 32+31 = 63: so 64 too high, so 49 = highest square
- possible squares are 4,9,16,25,36,49
- using 32: 32+4=36 and 32+17=49 are only possibilities

Hope someone solves soon, cause I'm now kinda stuck!!!

Good analysis. 4 and 17 do appear on each side of 32.

Enough variables for quite a few morning walks, but I am sure there will be an equation for this...