Filed under Math Trivia …

#math trivia #70 solution

Burt Kaliski Jr. (@modulomathy) 3/10/12 2:27 PM #math trivia for #March10: #70 is one of three tricomposites this month (products of three distinct primes). What are the other two? The three prime factors of 70 are, of course, 2, 5, and 7. March’s day-numbers range from 60 to 91. The other tricomposites among them are … Continue reading →

#math trivia #69 solution

Burt Kaliski Jr. (@modulomathy) 3/9/12 7:52 AM #math trivia for #March9: #69 can be expressed as the sum of three primes many ways, incl. 23+23+23. What are the other ways? The primes must all be odd, because 2+2 would have to be added to 65, which is not prime. The largest of the primes must … Continue reading →

#math trivia #68 solution

Burt Kaliski Jr. (@modulomathy) 3/8/12 7:21 AM #math trivia for #March8: #68 is both the sum of squares and the difference of squares. What are the squares? The sum of squares is 64+4, or 8^2+2^2. The difference is 324-256, or 18^2-16^2. General rule for the difference of squares: if an integer N can be expressed … Continue reading →

#math trivia #67 solution

Burt Kaliski Jr. (@modulomathy) 3/7/12 8:17 AM #math trivia for #March7: #67 divided by 366 = 1/p – 1/q + 1/r for p, q, r prime. What are the values of p, q and r? Start by expressing 67/366 as a sum of fractions: 67/366 = 61/366 + 6/366 = 1/6 + 1/61. The second … Continue reading →

#math trivia #66 solution

Burt Kaliski Jr. (@modulomathy) 3/6/12 7:14 AM #math trivia for #March6: #66 is “two of a kind”. What are the odds of getting “two of a kind” in a leap year? (Ignore leading 0s) The question is asking for the number of integers between 1 and 366 that have exactly two of some digit in … Continue reading →

#math trivia #65 solution

Burt Kaliski Jr. (@modulomathy) 3/5/12 1:05 PM #math trivia for #March5: #65 = (x^2-xy+y^2)(x+y) for positive integers x, y. What are x and y? (Hint: simplify the product.) Simplifying the product by multiplying the terms gives 65 = x^3+y^3 The solution is x = 4, y = 1, or vice versa.

#math trivia #64 solution

Burt Kaliski Jr. (@modulomathy) 3/4/12 8:08 PM #math trivia for #March4: #64 is one of only two sixth powers this year. How many days are nth powers for some n > 1? Seven days have numbers that are higher powers of 2: 4, 8, 16, 32, 64, 128, 256. There are four higher powers of … Continue reading →

#math trivia #63 solution

Burt Kaliski Jr. (@modulomathy) 3/3/12 5:08 PM #math trivia for #March3: #63 is not a #Mersenne prime but it’s divisible by two of them. Which ones? (Mersenne p = 2^q-1, p, q prime.) The day’s number, 63, has the form 2^6-1, but neither the exponent 6 nor the number 63 is prime. However, both prime … Continue reading →

#math trivia #62 solution

Burt Kaliski Jr. (@modulomathy) 3/2/12 9:09 PM #math trivia for #March2: #62 is 111110 base 2; with 5 ones this is “Hamming weight” 5. What other days this year have the same “weight”? The Hamming weight of an integer is the number of ones in its binary (base 2) representation. To find the different ways … Continue reading →

#math trivia #61 solution

Burt Kaliski Jr. (@modulomathy) 3/2/12 12:48 AM #math trivia for #March1: #61 is one sixth of the way through the year. Which other “sixths” come on the first day of the month? The last? A leap year has exactly six “sixths”, 61 days apart. With the usual alternation of 31- and 30-day months after February, … Continue reading →