Eureka: 2014

Wednesday, November 26, 2014

Contents as of November 26, 2014

The year is 2015 - Make equations:

Click on a topic:
Warm Up #1 problems 1 thru 10
Warm Up #2 problems 11 thru 20
Warm Up #3 problems 31 thru 40
Warm Up #4 problems 41 thru 50
Warm Up #5 problems 61 thru 70

How Mathematicians Count
Permutations & Tree Diagrams
combinations in lottery
Summer 2014 questions
The FORM of your ANSWERS...
You may need for Math Counts ...
Geometry Questions

Practice questions 151 thru 160
Practice questions 131 thru 140
Practice questions 121 thru 130

Equations using 2 0 1 4
Tough Problems 142,154,157,164,168-170,175,176,180
More Tough Problems 181,190 thru 194, 196 and 200
Successive Discounts
Math Quotes
Arrange numbers Puzzle
Find the missing number
Hit the target!
Separating the Turkeys
Graph Paper & Number lines for the Smartboard
What number belongs in each area so...
28 divided by 7 can't be 13! CAN IT?
142857 A Magic Number?
Number Fun!
Puzzle: Chess players
Puzzle:How many pages?
Alphametrics
Christmas Puzzles
Hints on solving equations...
Chaos with a ruler, die and pencil!
Combinations - Pascal's Triangle
Euler Paths - Circuits - Map Coloring
Team Questions (working together)
The Price is Right Games

MATH COMICS

(the sprint round questions are at the bottom...scroll down...)

Here is a useful site....
http://mathcountsnotes.blogspot.com/2011/12/mathcounts-competition-preparation.html

18) N is between Zero and 50

The Squares we are looking at are 28 more than N

and 100 more than N

Thus, these squares differ by 72

and they are between 28 and 150

The list of Squares to look at are:
36, 49, 64, 81, 100, 121, 144
The pair that differ by 72 are 49 and 121,

so N is 21.

****************************

19) Try a VENN DIAGRAM

with the HONOR ROLL circle

overlapping the SPORTS circle.

120 in the over lap
300 in the sports
P(in Honor Roll given in Sports)

= 120/300 = 2/5

Warm up #4 problems 41 thru 50

Doesn't #42 seem very similar to #19
http://mathyoucancounton.blogspot.com/2014/11/warm-up-2-problems-11-thru-20_13.html

(in #43) Notice that we are trying to find

a MULTIPLE of 101
that when ADDED to
a MULTIPLE of 19
gives the SUM 2015.
Take a look at the MULTIPLES of 101.
Their PATTERN may help you get
a partner that is a MULTIPLE of 19

If this question is too complicated,
then look at smaller squared arrangements:

4 dots gives ... squares
9 dots gives ... squares
etc.
OR WATCH THE SOLUTION (Click here!)

Graph the three points on the xy-plane.

The area FORMULA for a RIGHT TRIANGLE is

(1/2)(leg1)(leg2)

or use this crazy formula:

You may want to Pick a VALUE for X
and see what result it creates under the conditions of #50

Monday, November 17, 2014

Warm up #3 problems 31 thru 40

This is a straight forward problem. 6 factorial is =

6 times 5 times 4 times 3 times 2 times 1

so we can do the arithmetic. But reducing

the ANSWER will take time.

Take a look at this idea:

Divisible by 9
The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No

Recall #19 and the method we used:
http://mathyoucancounton.blogspot.com/2014/11/warm-up-2-problems-11-thru-20_13.html

Use enough decimals for PI

Hint: Draw a Rectangle 4 by 6
(Change into Inches!)

UNIT means 1
so each side of the BIGGER
SQUARES are 1 by 1

RULES FOR DIVISIBILITY:

A NUMBER IS DIVISIBLE BY_____, IF ______
2 The last digit is even (0,2,4,6,8)
128 is 129 is not
3 The sum of the digits is divisible by 3
381 (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3) No
4 The last 2 digits are divisible by 4
1312 is (12÷4=3) 7019 is not
5 The last digit is 0 or 5
175 is 809 is not
6 The number is divisible by both 2 and 3
114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
7 If you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 (Note: you can apply this rule to that answer again if you want)
672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No
8 The last three digits are divisible by 8
109816 (816÷8=102) Yes 216302 (302÷8=37 3/4) No
9 The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
10 The number ends in 0
11 If you sum every second digit and then subtract all other digits and the answer is: 0, or divisible by 11
1364 ((3+4) - (1+6) = 0) Yes
3729 ((7+9) - (3+2) = 11) Yes
25176 ((5+7) - (2+1+6) = 3) No
12 The number is divisible by both 3 and 4
648 (By 3? 6+4+8=18 and 18÷3=6 Yes.
By 4? 48÷4=12 Yes) Yes
524 (By 3? 5+2+4=11, 11÷3= 3 2/3 No.
Don't need to check by 4.) No

Thursday, November 13, 2014

Workout #1 Questions 21 thru 30

Workout #1 Questions 21 thru 30
The WORKOUT Questions are usually more difficult.
The one that are the most reasonable are:
24, 25, 26, 29
TRY THOSE FIRST