BMAD

The omitted rule is the smallest card beats (only) the highest card. Should we assume the students are now playing without that rule in effect? yes.

I saw a teacher mistakenly describe the rules to war as follows: each player receives five cards from the set of 1-10. They randomly pick a card to show the other opponent. The highest card turned over is the winner. The winner takes both cards and adds them to their collection to be used after shuffling their deck. She forgot the added rule that the highest card can be beat by the smallest card, the implications of this mistake should be obvious. Between two players what is the expected number of 'shows' needed before one player beats the other? also, note that in general i enjoyed the lesson by the teacher as the intent was to improve the students subitizing of number.

Can you explain what the 7th shape is meant to represent?

I am painting with red, yellow, and blue paint. All three colors will form 3 circles. When I used the red, i drew a red circle (disc maybe more appropriate as the circles were filled in with their colors) likewise for yellow and blue. The red circle had a diameter of 10cm, while the yellow and blue had 8cm and 6cm respectively. The circles were arranged thus: 1. The blue circle's ring touches the center of yellow 2. The yellow circle's ring touches the center of red 3. The red circle's touches the center of blue. For the sake of argument let's assume that red + blue + yellow = magenta. In terms of the painted area... what percentage of the shape is magenta? How many colors are represented in the painting?

Say we have two white pieces, bishop and knight. The bishop and knight are in their starting position, adjacent to each other. For the sake of argument, say the white bishop is on white. What square(s) on the board requires the most moves for either piece to reach?

is that why each weight is a multiple of three?

Anyone going to attempt the bonus? It extends with R have any number of elements and being able to 'make' any number. nice!

yes but i did find a typo. i meant R=A+B+C+D

At age zero, 0 / 2 = 0

Suppose there is a rock, R. It's weight is known to be 40 lbs. The store owner uses the rock to measure out purchases; in other words, customers bought 40 lbs of an item when making a purchase. He would load the rock on one end of a scale and the food on the other until they are even then the transaction occurs. One day, the clerk drops the rock and it breaks into exactly four distinct pieces (e.g. R= A+B=C+D), At first he thought he was in trouble as he may not have any way to sell his items. But fortunately he found that he can still stack all 40 lbs on the same side of the scale to complete a 40 lb purchase. Additionally, he found that he can now use the various pieces on different sides of the scale to allow for a customer to buy products anywhere from 1 to 40 lbs ultimately bringing in even more customers. If A>B>C>D >0 prove A-B-C-D > C-D bonus points if you can explain (warning gives the answer away)...

Ah. I see my mistake completely now. I will retell the puzzle with all the information this time.

weird. my exponents did not work. 62014 should have been 62013

How many positive integers divide 62014 but not 62013?

I. suppose that for all reals 0 <= a <= b <= c <= d , we have: (a + b + c + d)^2 >= K b c . Find the largest possible value of K II. Suppose a + b + c = 1 , where a , b , and c are non-neg. real nos. Prove that we always have: 7(a b + a c + b c) <= 2 + 9 a b c .

please help me find the flaw in my reasoning...

I realized that, which is why I added my second post. :-D

4, 6, 12, 18, 30, 42, 60, 72, 102, 108, ... 4+2(n-1)+2(n-1)(n-2)-(4/6)(n-1)(n-2)(n-3)... Continue in this fashion to build all the terms then slap on any scalar along with (n-1)...(n-10) to generate infinite endings Note:n=1 gives 4

Interesting. I found a different solution and I thought my solution was unique.

Assume that a+b+c+d=40

If If a,b,c,d are natural numbers and and a > b > c > d > 0 then show that a - b - c -d > c - d .... To the moderators, this text box does not show up on my Ipad.

Proof by contradiction

Prove that if a, b, and c are odd integers, then a x^2 + b x + c = 0 has no rational roots.

There were six prices for various TV sets sold at the store: $231, $273, $429, $600.60, $1001, and $1501.50. One day, a motel owner came in and bought a bunch of TVs. The total came to $13519.90 but the bill of sale was lost. How many of each TV type did the motel guy buy?