The New Terra Nova

If you were traveling to what is today called Newfoundland in the late 15th or early 16th century, you might be an Italian explorer on an expedition from England, or an English, French, Portuguese or Spanish fisherman, en route to “Terra Nova,” the New Found Land. And if it was 500 years earlier, it turns out, you … Continue reading →

#math trivia #134 solution

#math trivia for #May13:  #134 and its prime divisors (67, 2) have no common digits.  When did this last happen?  When will it happen again? Answer:  This is a fun problem that can be solved with by trial-and-error moving forward and backward from 134, using some properties of factorizations to shorten the search. Clearly, a … Continue reading →

#math trivia #133 solution

#math trivia for #May12:  #133 has the form xyz where xyz is one more than a multiple of yz (133 = 4*33+1).  Which other day-numbers do? Answer:  If xyz is one more than a multiple of yz, then x00 = xyz = yz is also one more than a multiple of yz.  This means that … Continue reading →

#math trivia #132 solution

#math trivia for #May11: #132 can be expressed in three ways as the product of positive integers x, y where x-y is a square.  What are they? Answer:  Consider the possible factorizations of 132 into x*y: 132*1 66*2 44*3 33*4 22*6 12*11 The three factorizations where x-y is a square are 66*2, 22*6, and 12*11.

#math trivia #131 solution

#math trivia for #May10:  #131 is a prime, 13 is a prime, and 31 is a prime.  For what other day-numbers xyz are xyz, xy and yz all prime? Answer:  This is a good pattern matching problem.  The shortest approach is probably to look at prime xy values and see which z’s work.  We’ll allow … Continue reading →

#math trivia #130 solution

#math trivia for #May9:  #130 can be expressed with two 1s and the rest (if any) all 0s in what bases? Answer.  This is equivalent to asking for which bases b can 130 be expressed as 130 = b^x + b^y for distinct x, y.  Without loss of generality, let y be the smaller of … Continue reading →

#math trivia #129 solution

#math trivia for #May8: #129 is another prime of the form 2^x+1. How many others will be encountered this year? — Burt Kaliski Jr. (@modulomathy) May 8, 2012 Nine day-numbers have the form 2^x+1:  2, 3, 5, 9, 17, 33, 65, 129, and 257.  Of these, six are prime:  2, 3, 5, 17, 129 and … Continue reading →

#math trivia #128 solution

#math trivia for #May7:  Similar to #127:  How can #128 be computed from 1, 2, and 8 using only two operations from +, -, *, /, ^? — Burt Kaliski Jr. (@modulomathy) May 7, 2012 There’s a small trick:  You have to use either parentheses or superscripts. 128 = 2^(8-1) or 128 = 28-1

#math trivia #127 solution

#math trivia for #May6: How can #127 be computed from 1, 2, and 7 using only two operations from +, -, *, /, and ^ (exponentiation)? — Burt Kaliski Jr. (@modulomathy) May 6, 2012 Having exponentiation as an operator helps out here, because 2^7 = 128.  The answer is 2^7 – 1 = 127   … Continue reading →

#math trivia #126 solution

#math trivia for #May5: #126 is one of 40 day-numbers divisible by 9. How many of the 40 also have a digit-sum of 9? — Burt Kaliski Jr. (@modulomathy) May 5, 2012 Every number divisible by 9 has a digit-sum that’s also divisible by 9.  For most small numbers divisible by 9, the digit-sum is … Continue reading →