New-York tribune., 1910-02-13
AN ODD FEATURE OF 1s.les, ETC.

AN ODD FEATURE OF ~ 1872 EN-
A SHORT time ago. the author Of this article
Wrote for YOUR SUNDAY MAGAZINE an dT'l-
,-1, entitled " Nurlicr 9l an OddItv."
The reverse number 10 also has an odd tca-
11.re when used to multiply number OF two
places with the same figure IN caCh place. or
IN other words, the first nine multp.es ct II,
7z- II - 30 ~ -. G6, a. -, and 90.
! ct MS r.I,,. IL times 10 The hundreds figure
Of the 1rod1lct may lc found by adding the two
l. in IL which makes ,, while the ten and
unit figures viii bc the product oi the UNITS OF
both numbers, thus, times IS > AS therG
Is also one figure in this product, however, ana
yye must have two places, we prehN a GlphGr'
making % and the whole product VIII then be
2O9
Likewise the product OF % times 10 VIII be
as follows The sum Of the 2's IN % gives
hundreds: and the product Of the UNITS
time Q IS Is: and the total product IS therefore
ilA
In the same manner the product OF ;5;5 time
10 may he found - be 624 A ilrntS ~ 500
and SO on to % times 10, or ISL The prl1!o
1l, however ends here and cannot be e>teIdtb
10 hjgfcr rnu1IirJeS Of II, except OF course ilo
hines 10 where the product Is SIMPLY clI'heI
annexed To the rrodrct Of ii times ~
\ slight variation Of this VIII extend the pm
cir,1t. t. rnutipl vIng number OF three places o
the same figure (the first nine nult1pitS OF III
bv 1873 This may be illustrated as follows
Multiply 222 by l99. For the hundred and
TINT figIIres Of the product We mulupIy 10,
get
TlluItipIIcr , and 9, which gives IS for zen,
+5,,1rt- between hundreds and units, we take |
l,-e- than units figure. gIs :. The night h4hd
rpsrt uf the product VIII therefore hc I'N- Ioi
The remaining left hand figures OF the pT"ducl'
W.. ,7r.lrirIZ the places Of the mut1pliCa1ld az
-. 1.f- - --r,l+s [.-- - by >, which gives "a
The complete product VIII therefore bc fl'0-
For :, :f:}3 rjTlcs 999 where the figure IS re
pe..tcd four times IN the mulilpllCald me 'lF
i changed 50 that the figures IN thc lf"duc' -
~..rds and units place. the intervening P,i,'S
hundreds and tens each beng occupied bt "
.5,,-r, ! L. rT.n units The night hand portion
af The product viii therefore be Zoh'- we 5'io!i
1,l,ll-I-,v al the figures oI the mhIu
,r,r unit bv , which gives G66 for the let part
Til-..,iis. numbers Of five places containing
-l, SAM, figure five times can he mu''lpLl'h 10y
10 9g9 number Of SIX places by l9'''' -
n. rgr1tir,l.ing ~ the figures oi the ilu.'lI'l
.5nd except units bv , for the LETT P'T''D,h ~
The r,~ga5llt and mutiplv ing units OF mII'lIl-
.suf Bl- units IF mul1Iplcr- placing me lI4ui's
So, +.r,7E ~ the places ot the product core
spending t. the end place "l iI4i.' l'''' "
rfllltirlier filling the nt"TIh''lt'| I'''''
,.-.-I ti.,r1r- les than units Of product.
T. illustrate the rule more th"r"n&hIE' ie' uS
Tie tIl,. ,.,..rlt,lt. II i44 times 1888. ACc"TH
j1f, to the rule We have for the let p"Iii"il 81
th, product ! 444 times ,, or : $50. ~ ~. W..
r:ghf hand tiglreS we have . tunes ! "i DO
occupying then thousands ana uInt5 ll','a ~
The fraIu.r ftb,- end places Of both mnItiIh-
.srj and rnultirylier being ten thousands ana
1lrItsl tn, Intermediate figure beng minus l.
q , repeated three times for thousands nun
drcds. and tens places OF products ! ne &c com
Tlete product viii therefore be SNN,A'f3,o3o
The rule Is really very simple when thoT-
oughl.. understood and. beside beng interest
lug and odd shows how a large operation IN
multiplying such class "f nnmhyTs may De
simpllfrd -DaOIghi s IisemaH