270 Answersthere any remainder? No. (3) If you divide again by 2, is there any remainder?
No. Your twenty questions will be all the same, and writing from right to left,
you put down a zero for the answer "No," and 1 for the answer "Yes." The re-
sult will be that after the twentieth question you will get 11001101111111000000.
This is 843,712 written in the binary scale. Dropping the final 0 in the units
place, the first 1 is the sixth figure backwards. Add together the 6th, 7th, 8th,
9th, 10th, lith, 12th, 14th, 15th, 18th, and 19th powers of 2 and you will get
843,712 in our denary scale.
If the number is a low one like 100,000, seventeen questions would be suffi-
cient if only you knew that the 0 had been reached in the quotient, but the
three final questions will merely add three noughts to the left of your binary
number. But to prevent quibbles as to infinities, etc., it is best to state before
beginning your questions that zero divided by 2 is understood to mean zero
with no remainder.
- A CARD TRICK
Every pile must contain 13 cards, less the value of the bottom card. There-
fore, 13 times the number of piles less the sum of the bottom cards, and plus
the number of cards left over, must equal 52, the number in the pack. Thus
13 times the number of piles plus number of cards left over, less 52, must
equal sum of bottom cards. Or, which is the same thing, the number of piles
less 4, multiplied by 13, and plus the cards left over gives the answer as
stated. The algebraically inclined reader can easily express this in terms of his
familiar symbols.- THE QUARRELSOME CHILDREN
Each parent had three children when they married, and six were born
afterward.
185. SHARING THE APPLES
Ned Smith and his sister Jane took 3 and 3 respectively, Tom and Kate
Brown took 8 and 4 respectively, Bill and Anne Jones took 3 and 1 respec-
tively, and Jack and Mary Robinson took 8 and 2 respectively. This accounts
for the 32 apples.