ENGR. BESAVILLA’S NOTES
Problem 130 Problem 137
Assume the universe is a billion billion light years in diameter and is packed Starting with one, place each succeeding integer in one of two groups such
solidly with matter weighing a billion billion tons per cubic inch and each that neither group contains three integers in arithmetic progression. How far
gram of this matter contains a billion billion atoms. Also, every second during can you get?
the past billion billion years, a billion billion similar universes were created.
Without using any symbols and restricting yourself to a total of three digits, Ans: First 8 integers
write a number that far exceeds the total atoms of all these universes.
9 Problem 138
Ans: 99 In a lottery the total prize money available was a million dollars, paid out in
prizes which were powers of $11 viz., $1, $11, $121, etc. Noe more than 6
people received the same prize. How many prize winners were there, and
Problem 131
how was the money distributed?
The sum of the digits on the odometer in my car (which reads up to 99999.9
miles) has never been higher than it is now, but it was the same 900 miles Ans: 20 winners
ago. How many miles must I drive before it is higher than it is now?
Ans: 100 miles Problem 139
In the arithmetic of Puevigi, 14 is a factor of 41. What is the base of the
number system?
Problem 132
Ans: 11
The first expedition to Mars found only the ruins of a civilization. The
explorers were able to translate a Martian equation as follows:
⎧ Problem 140
5x 2 − 50x +125 = 0 x = ⎨ 5 . This was strange mathematics. The value Find the only number consisting of five different digits which is a factor of its
⎩ 8
reversal.
x = 5 seemed legitimate enough but x = 8 required some explanation. If the
Martian number system developed in a manner similar to ours, how many Ans: 87912
fingers would you say the Martians had?
Ans: 13 Problem 141
Barnie Bookworm bought a thriller – found to his dismay,
Just before the denouement a fascicle astray.
Problem 133 Instead of counting one through ten, a standard cure for rages.
A rectangular picture, each of whose dimensions is an integral number of He totalled up the number of the missing sheaf of pages.
inches, has an ordinary rectangular frame 1 inch wide. Find the dimensions The total was eight thousand and six hundred fifty-six.
of the picture if the area of the picture and the area of the frame are equal. What were the missing pages? Try to find them just for kicks,
Ans: 3 x 10 or 4 x 6 Ans: 255 – 286 are missing pages
Problem 142
Problem 134 The Sultan arranged his wives in order of increasing seniority and presented
Find unequal rational numbers, a, b, (other than 2 and 4) such that ab = ba. each with a golden ring. Next, every 3rd wide, starting with the 2nd, was given
a 2nd ring; of these every 3rd one starting with the 2nd received a 3rd ring, etc.
Ans: a = 9/4
His first and most cherished wife was the only one to receive 10 rings. How
b = 27/8 many wives had the Sultan?
Ans: 9842 wives
Problem 135
My house is on a road where the numbers run 1, 2, 3, 4… consecutively. My
number is a three digit one and, by a curious coincidence, the sum of all Problem 143
house numbers less than mine is the same as the sum of all house numbers A certain magic square contains nine consecutive 2-digit numbers. The sum
greater than mine. What is my number and how many houses are there on of the numbers in any line is equal to one of the numbers in the square with
my road? the digits reversed. This is still the case if 7 is added to each entry. What is
the number in the center square?
Ans: house number = 204 Ans: 17
no. of houses = 208
Problem 144
Problem 136 Obviously the smaller the compounding period, the greater the interest. How
On what days of the week can the first day of a century fall? (The first day of much does one dollar amount to after one year at 100% per annum interest,
the twentieth century was Jan. 1, 1901) compounded continously, i.e., instantaneously?
Ans: Monday Ans: $2.71
Problem 130 Problem 137
Assume the universe is a billion billion light years in diameter and is packed Starting with one, place each succeeding integer in one of two groups such
solidly with matter weighing a billion billion tons per cubic inch and each that neither group contains three integers in arithmetic progression. How far
gram of this matter contains a billion billion atoms. Also, every second during can you get?
the past billion billion years, a billion billion similar universes were created.
Without using any symbols and restricting yourself to a total of three digits, Ans: First 8 integers
write a number that far exceeds the total atoms of all these universes.
9 Problem 138
Ans: 99 In a lottery the total prize money available was a million dollars, paid out in
prizes which were powers of $11 viz., $1, $11, $121, etc. Noe more than 6
people received the same prize. How many prize winners were there, and
Problem 131
how was the money distributed?
The sum of the digits on the odometer in my car (which reads up to 99999.9
miles) has never been higher than it is now, but it was the same 900 miles Ans: 20 winners
ago. How many miles must I drive before it is higher than it is now?
Ans: 100 miles Problem 139
In the arithmetic of Puevigi, 14 is a factor of 41. What is the base of the
number system?
Problem 132
Ans: 11
The first expedition to Mars found only the ruins of a civilization. The
explorers were able to translate a Martian equation as follows:
⎧ Problem 140
5x 2 − 50x +125 = 0 x = ⎨ 5 . This was strange mathematics. The value Find the only number consisting of five different digits which is a factor of its
⎩ 8
reversal.
x = 5 seemed legitimate enough but x = 8 required some explanation. If the
Martian number system developed in a manner similar to ours, how many Ans: 87912
fingers would you say the Martians had?
Ans: 13 Problem 141
Barnie Bookworm bought a thriller – found to his dismay,
Just before the denouement a fascicle astray.
Problem 133 Instead of counting one through ten, a standard cure for rages.
A rectangular picture, each of whose dimensions is an integral number of He totalled up the number of the missing sheaf of pages.
inches, has an ordinary rectangular frame 1 inch wide. Find the dimensions The total was eight thousand and six hundred fifty-six.
of the picture if the area of the picture and the area of the frame are equal. What were the missing pages? Try to find them just for kicks,
Ans: 3 x 10 or 4 x 6 Ans: 255 – 286 are missing pages
Problem 142
Problem 134 The Sultan arranged his wives in order of increasing seniority and presented
Find unequal rational numbers, a, b, (other than 2 and 4) such that ab = ba. each with a golden ring. Next, every 3rd wide, starting with the 2nd, was given
a 2nd ring; of these every 3rd one starting with the 2nd received a 3rd ring, etc.
Ans: a = 9/4
His first and most cherished wife was the only one to receive 10 rings. How
b = 27/8 many wives had the Sultan?
Ans: 9842 wives
Problem 135
My house is on a road where the numbers run 1, 2, 3, 4… consecutively. My
number is a three digit one and, by a curious coincidence, the sum of all Problem 143
house numbers less than mine is the same as the sum of all house numbers A certain magic square contains nine consecutive 2-digit numbers. The sum
greater than mine. What is my number and how many houses are there on of the numbers in any line is equal to one of the numbers in the square with
my road? the digits reversed. This is still the case if 7 is added to each entry. What is
the number in the center square?
Ans: house number = 204 Ans: 17
no. of houses = 208
Problem 144
Problem 136 Obviously the smaller the compounding period, the greater the interest. How
On what days of the week can the first day of a century fall? (The first day of much does one dollar amount to after one year at 100% per annum interest,
the twentieth century was Jan. 1, 1901) compounded continously, i.e., instantaneously?
Ans: Monday Ans: $2.71
