# Posted in June 2012 …

## #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

## #math trivia #125 solution

#math trivia for #May4: #125 divides 1000. What other day-numbers divide a power of 10? What’s the general pattern these numbers follow? — Burt Kaliski Jr. (@modulomathy) May 4, 2012 The day-numbers that divide a power of 10 (and the power they divide) are: 1 — 1 2 — 10 4 — 100 5 — … Continue reading

## #math trivia #124 solution

#math trivia for #May3:  How many day-numbers, like #124, have the property that the no digit is larger than the one’s digit? — Burt Kaliski Jr. (@modulomathy) May 4, 2012 This is a little different than the answer to #123, where the digits had to be in increasing order.  (And to be clear, the “the” … Continue reading

## #math trivia #123 solution

#math trivia for #May2:  The digits of #123 are in increasing order:  1 < 2 < 3.  How many other numbers 1-366 have this arrangement? — Burt Kaliski Jr. (@modulomathy) May 2, 2012 We’ll start by assuming that single-digit numbers have their single digit in increasing order.  9 numbers so far. Among the two-digit numbers, … Continue reading

## #math trivia #122 solution

#math trivia for #May1: #122 reversed is #221, also a day-number (1-366). How many day-numbers have this property? (Leading 0s not allowed.) — Burt Kaliski Jr. (@modulomathy) May 1, 2012 All of the one-digit day-numbers, 1-9, when reversed, are themselves, so have the property.  That’s 9. All of the two-digit day-numbers, 10-99, when reversed, are … Continue reading

## #math trivia #159 solution

#math trivia for #June7:  #159 is the product of 3 and 53, two primes with the same last digit. What other day-numbers have this property? — Burt Kaliski Jr. (@modulomathy) June 8, 2012 One of the primes must be less than or equal to the square root of 366, i.e., 19 or less.  We can … Continue reading

## #math trivia #158 solution

#math trivia for #June6: #158 is the sum of which three squares?  (There can be more than one answer.) — Burt Kaliski Jr. (@modulomathy) June 7, 2012 Answer:  158 can be expressed as the sum of three squares two ways: 158 = 100 + 49 + 9 158 = 121 + 36 + 1