Filed under Math Trivia …

#math trivia #101 solution

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 →

#math trivia #100 solution

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 →

#math trivia #99 solution

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 →

#math trivia #98 solution

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 →

#math trivia #97 solution

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 →

#math trivia #96 solution

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 →

#math trivia #April4 solution

Burt Kaliski Jr. (@modulomathy) 4/4/12 7:14 PM #math trivia for #April4: How many times this year do month and day both divide into year (’12)? In what year does this happen most often? Another non-day-number problem, similar to #April3. Both day and month divide into year 36 times in ’12: whenever both are among the … Continue reading →

#math trivia #April3 solution

Burt Kaliski Jr. (@modulomathy) 4/3/12 7:34 AM #math trivia for #April3: day*month = year today. How many other days does this happen in ’12? Is there any year with more “product” days? This problem, unlike most (but like the next one) is about the actual date, not the day-number (which would be #94). The other … Continue reading →

#math trivia #93 solution

Burt Kaliski Jr. (@modulomathy) 4/2/12 9:45 AM #math trivia for #April2: #93 can be checked for divisibility by 3 by adding the digits and checking the sum. Why does this test work? The classic test for divisibility by 3 is to add the digits of a number and test if the sum is divisible for … Continue reading →

#math trivia #92 solution

Burt Kaliski Jr. (@modulomathy) 4/1/12 10:35 PM #math trivia for #April1: #92 = 7*13+1, so April is congruent to January; both start on Sunday. What other months are congruent this year? The answer is a simple matter of modular arithmetic. Reduced modulo 7, the lengths of the 12 months in a leap year follow the … Continue reading →