Evening star. [volume] (Washington, D.C.) 1854-1972, 1908-10-18

remainders. Multiply the first remainder
by 40, the second by As, and the third by
SO. Add the three products, and divide
the sum by 60. and the remainder will
be the number first thought of. Thus, start
with 4s. Dividing by g.. 4, and 5 will
give remainders OF /, 8, and 3. Multiplying
these by 40, As and sc respectively, will give
40, 1876, and 1903. The sum of these three
numbers is 2S3, which will give remainder of
43, the original number, when it is divided by 60.
About 1912 the following problem ap-
peared: Let some one called A select any
number of counters. Let another person. B,
take p times as many where you choose the
value of p. Then let A give counters to B
A p times the number has left. B will then
have q (p plus ~ counters left. Thus, sup
pose you assign the value of to q, and 3 to p.
Suppose A selects counters. takes IS. A
gives B ?, making II for and 3 for A. B then
gives or,3 times or g. which leaves him 8.
Then Up plus y is equal to 6 plus ~ or
times 4, which is 8. the number that B still has
in his possession
Solving by Reversal
A CURIOUS result is seen in the following
= Take any three digits; reverse them, and
find the difference between the two values. Re
verse this difference and add the reversed diff
ference to the first difference, and the result
will always be 1,oSo. Thus. take o87; reverse,
and we get $50. The difference is 1913; the
reversed difference is Sol. The sum of 18o and
Sol is 1850.
Take any two numbers. one odd and the
other even. Let A select either number, and
B the other. You can tell which number A
selects by this method: Ask A to multiply his
number by 2, and B to multiply his by 3.
Tell them to add the two products and tell the
sum. If the sum is odd, A chose the even num-
Der; but if it is even, then A chose the odd
number.
A more modern problem is the following:
Ihnncn cr,u 11O1fc
of the digits and get the difference. If the
first or last digit of the difference is known,
you can always tell the entire difference, since
the difference will always have for its middle
figure O. Then if the first figure of the difference
is known, the third is always 9 minus the first;
in the same way the first is always minus the
third. If either the first last figure is 9, the
difference is 90. Thus, take 756. Reverse and
get 657. The difference is 90. If we take S53
and reverse. we get ;358, and the difference is
4os Since the sum Of the first and last digits
of the difference is Q, the other one can be told
when either is known.
EDWARD ROTH of Philadelphia, comment
- ing on one of Mr.. Emerys earlier articles
on Tricks with Numbers" writes:
Your mathematical correspondents GER
tainly know a good deal about the curiosities
of arithmetic; but do they know of anything
more singular than the following combination?
LILO, 40, 588, 235,2o4
Multiplied by 2, this gives: 2,352,o41,176,
40, 5Ss, which is exactly the same figures over
again in almost exactly the same order, being
taken from the middle and set in the unit
place.
Multiplied by 3, it gives: 3,52o,41I,764,
7o5,SS2, which, as far as figures go, is exactly
the same as before, being made the unit.
Multiplied by 4, it gives: 47o5,SS2,352,-
941,I76, figures still the same, and in the same
order, only is made the unit.
Multiplication by any Arabic digit will
u;,r c,,,;1ar This I
before. and came on it by accident"