The figure gives the formula for m consecutive numbers.
Here we have m+1=5 and m=4 .
In this case 265 = (5/2)x(2xn + 4) & 106 = 2xn + 4 & 2n= 102 & n=51 & the gratest of them 51+4 = 55 & 55/15 = 11 .
But this is the formal way to solve; in tests time is scarce. Look at the second tip and ry1 .
As is in ry1, in case we have an odd number of numbers, sum divided buy number gives the midddle term.
If it is demanded "k" cents for the first copy, k + 11 x (k30) cents will be demanded for 12 copies.
Use of trial and error can laso be made:
Since this is a pretty hard nut for 4th graders, trying the easiest to handle choice we get: the first is 100 cents, and 11x70=770 cents for the others .
The sum will not be even for "b".
Numbers in "a" are not consecutive.
Let the first number be n .
The second will be 2 x (n+1) and the sum n + 2x(n+1) = 212 .
In case of trial and error:
"a" and "b" are excluded (the first tip) .
Suppose "c" is true; first no. is 80 and second term of the sum is 2x81=162. Fails.
For each natural number n: n+(n+1)+(n+2) = n+3
3xn + 3 = 5xn  2 i.e. 2xn = 5 must ve valid but can not be for natural numbers !
3n + 3 = 5n  3 i.e. 2xn = 6



OUR GENERATION, GENERATION 1968, AND CONSECUTIVES MAKE A GREAT ERROR.
AN ERROR THE GENERATION 2020 AND CONSECUTIVES WILL PAY FOR.
AN ULTRAMODERN BOEING JET IS IN THE NEIGHBORHOOD OF ... AIRPORT IN EMERGENCY.
 MAYDAY, MAYDAY. OUR OUTER LEFT MOTOR GOT FIRE.
 NO PROBLEM, YOUR AIRCRAFT IS OF PERFECT TECH.
 THE INNER LEFT GOT ALSO FIRE.
 NO PROBLEM, YOUR AIRCRAFT IS OF PERFECT TECH.
AFTER A WHILE
 I REPEAT, MAYDAY. OUR INNER RIGHT MOTOR GOT FIRE.
 NO PROBLEM, YOUR AIRCRAFT IS OF PERFECT TECH. ONE MOTOR IS ENOUGH.
 MAYDAY, MAYDAY. OUR OUTER LEFT MOTOR GOT FIRE!!!
WE DO NEED EMERGENCY HELP !!! UNDERSTOOD !!!???
 UNFORTUNATELY TOO LATE FOR IT; PLEASE TURN YOUR LOUDSPEAKERS ON AND REPEAT ALL AFTER ME "GOOD LORD
WE, YOUR SONS, ARE ALMOST TO TAKE THE WAY TO YOU AND YOUR MERCY, PLEASE FORGIVE US ....


Let there be 14 steps between floors; Ali has two possiblities:
a Beginnin with onebyone she will set her foot on 14, 7 , 14, 7 and 14 steps between floors consecutively which gives a total of 56 steps.
b Beginnin with twobytwo she will set her foot on 7, 14, 7, 14 and 7 steps between floors consecutively which gives a total of 49 steps.
Let there be 15 steps between floors; Ali has two possiblities : ...
2xn+1 + 2xn+3 + 2xn+5 = 6xn + 9 = 4xn + 10 + 13 i.e. 2xn + 1 = 23  8.
(90 + A)/2 = 85 & A=?
There are 16 adults including Mrs. Transperent .
For each adult P g. => Px16 + (P60)x15 = 3750 => 31xP = 4650 .
Remember oneoone, oneotwo, ... etc. .



YEHUDI MENUHIN SHOULD HAVE SAID :"IF I DO NOT PLAY FOR A DAY, I FEEL; IF I DO NOT PLAY FOR A WEEK, MY AUDIENCE FEELS ..."
A CONVERSATION BETWEEN TWO DIPLOMATS OF TWO DIFFERENT COUNTRIES:
 WHAT IS THE DIFFERENCE BETWEEN YOUR CITIZENS AND SPENDTHRIFTS ?
 WELL, NOT A POLITE QUESTION, MAY I TAKE YOUR ANSWER ?
 SURE, ONE SPENDS THAT EXIST; THE OTHERS NON EXISTING ...
AFTER A WHILE THE OTHER DIPLOMAT ASKS THE FIRST AND ...
 WHAT IS THE DIFFERENCE BETWEEN YOUR CITIZENS AND SPENDTHRIFTS ?
 WELL, I CAN NOT SAY EXACTLY, MAY I TAKE YOUR ANSWER ?
 SURE, ONE SPENDS THAT EXIST; THE OTHERS TO MAKE EVERYTHING, THE WHOLE WORLD, DISTINCT ...
In this case the coding has base 9 (0 + 8 digits).
The place value of the outermost left digit is 9^{2}=81 ,
the place value of the middle digit is 9 and
the place value of the outermost right digit is 1 .
prime exactly divisible only by 1 and itself. 1 is not prime by definition.
61 is relly prime.
60 is not divisible by 8 without remainder.
11x606 = 6666 .
One possible combination is 2x25 cents, and another combination may be 25 cents, 10 cents, 10 cents and 5 cents .
This is the feedback!