You are competing in a game with 2 other players with a 21-faces dice (labeled 1-21). all three of you gets to choose a number and then roll the dice. whoever chose the number closest to the outcome wins. what is your strategy?

This is actually an interview question for IT jobs!

The game strategy changes if there can be communication or not.

If there is no communication then I would pick the expected value of the game, meaning the sum of each value times the probability of it showing up on the die (1/21) or:

=

This mathematically minimizes the difference between my pick and the one that comes from the roll.

If there is communication, and a consensus can be reached, then the most reasonable answer would be the one that gives all of us the same possibility to win: 4, 11, 18, so each of us covers 7 numbers, and each of us would have 1/3 chances to win.

If there is communication, and a consensus cannot be reached, then I would have to calculate the difference between both their pics, if it is smaller than the expected value, and it inclines towards high numbers, for example: 10, 18, then i would pick one less than the smallest, meaning 9, because i would cover 1-9, the one picking 10 would cover 10-14 and 18 would cover 15-21. My range would be bigger. If it is smaller than the expected value, and it inclines towards low numbers, i would pick one over the highest, for example 4, 9. I would pick 10. If the difference is bigger than  the expected value then i would calculate whether i would cover more picking a number in the middle of their range or to the side, depending on their pick. For example, if they pick 9, 21, I would cover more range picking 8 than 15.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24