#math trivia for #April13: Second #FridayThe13th this year. Is there a third?What’s the most a year can have? The fewest? — Burt Kaliski Jr. (@modulomathy) April 13, 2012 This one is related to the answer to #92. The starting days of the month, as noted in that answer, have the following modular values (relative to January 1) … Continue reading →

#math trivia for #April12:#103 and 263 are primes that sum to 366.How many other ways can 366 be expressed as the sum of two primes? — Burt Kaliski Jr. (@modulomathy) April 12, 2012 There are 17 other ways (determined with the help of a spreadsheet): 7 359 13 353 17 349 19 347 29 337 … Continue reading →

#math trivia for #April11:  #102 contains three consecutive digits.  How many other numbers 100-366 have this property? — Burt Kaliski Jr. (@modulomathy) April 12, 2012 The simplest way is probably to look at the eight different possible sets of digits involved: 0,1,2:  102, 120, 201, 210 (4 ways) 1,2,3:  123, 132, 213, 231, 312, 321 … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/10/12 7:49 PM #math trivia for #April10: #101 is one of six day-numbers this year whose digits sum to 2. What are the others? What’s the most common sum? The other day-numbers with a digit-sum of 2 are 2, 11, 20, 110, and 200. The most common digit-sum is 10, which … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/9/12 8:19 AM #math trivia for #April9: In _signed decimal_, digits have values from -10 to +9. What’s another way to represent #100 in this notation? The usual way to represent 100 is with unsigned digits: 100 = 1*10^2 + 0*10^1 + 0*10^0 Another way to represent 100 is with signed … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/8/12 9:32 PM #math trivia for #April8: #99 is the last two-digit number this year. How many digits do the 366 days this year have overall? Overall, the 366 day-numbers this year have 990 digits: — 9 days have one digit — 9 total — 90 have two — 180 more … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/7/12 11:55 AM #math trivia for #April7: #98 is the product of a number and its double. What’s the number, and what product near 10000 has this property? The number is 7: 7*14 = 98. Consider the equation 2x^2 = 98. The product near 10000 with this property is 71*142 = … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/6/12 9:42 AM #math trivia for #April6: #97 is the largest prime less than 100. Are primes more likely than average to occur very close to a power of 10? “Average” here can be understood to refer to the probability that a random number “in the vicinity” (but not necessarily “very … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/5/12 8:25 AM #math trivia for #April5: #96 ties record for prime factors counting repeats (6), but doesn’t match record for divisors (12). Why not? The six prime factors of 96, counting repeats, are 2, 2, 2, 2, 2, and 3. This ties 64, which is the product of six 2s. … Continue reading →