Optimal algorithms for mastermind and bulls-cows games.
... number of turns is arbitrary (six turns is enough) and 5626/1296=4.34 is we can do maximum five turns. For this optimization type we construct three optimal algorithms one for bulls-cows game and two for mastermind game. Minimal amount of numbers. It’s known for bulls-cows game that there is no algo ...
... number of turns is arbitrary (six turns is enough) and 5626/1296=4.34 is we can do maximum five turns. For this optimization type we construct three optimal algorithms one for bulls-cows game and two for mastermind game. Minimal amount of numbers. It’s known for bulls-cows game that there is no algo ...
Answer
... Quiz scores The quiz scores for a math class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Identify an extreme value and describe how it affects the mean. The data value 0 appears to be an extreme value. Calculate the mean with and without the extreme value to find how it affects the mean. ...
... Quiz scores The quiz scores for a math class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Identify an extreme value and describe how it affects the mean. The data value 0 appears to be an extreme value. Calculate the mean with and without the extreme value to find how it affects the mean. ...
6th Grade Even and Odd Numbers
... A multiple of a whole number is the product of the number and any nonzero whole number. A multiple that is shared by two or more numbers is a common multiple. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ... Multiples of 14: 14, 28, 42, 56, 70, 84,... The least of the common multiples of two or mo ...
... A multiple of a whole number is the product of the number and any nonzero whole number. A multiple that is shared by two or more numbers is a common multiple. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ... Multiples of 14: 14, 28, 42, 56, 70, 84,... The least of the common multiples of two or mo ...
Amazing properties of binomial coefficients
... But it should be accurate in cases when p − 1 divides j or k, because the induction hypothesis does not hold for j = 0 or k = 0 (it uses the value p − 1 instead of 0). Therefore we must consider more carefully the cases when j = 1 or k = 1. We restrict ourselves by consideration of one partial case ...
... But it should be accurate in cases when p − 1 divides j or k, because the induction hypothesis does not hold for j = 0 or k = 0 (it uses the value p − 1 instead of 0). Therefore we must consider more carefully the cases when j = 1 or k = 1. We restrict ourselves by consideration of one partial case ...
