Puzzle 5
Combine the word fragments below to produce pairs of words that have opposite meanings. There are 9 pairs of words, one pair on each line.
For example, USE REF EPT ACC becomes ACCEPT + REFUSE.
AB ANT RCE SCA UND
WA RY RD BR ICE CO AVE
ETY NG SAF ER DA
ACT AND CO EXP NTR
WN US UNK NO MO FA
TR TE IBU HER GAT DIS
CAL HO RI RTI TAL VE ZON
TIO AL CID EN ENT INT NAL AC
OWL OR KN IGN GE ED CE AN
Puzzle Copyright © Elliott Line
This puzzle appeared in Mensa's EnigmaSig (194.21) and is used with permission.
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Hint
The first letters of one half of the words are: A, B, D, C, F, D, H, A, I.
Answer
ABUNDANT + SCARCE
BRAVERY + COWARDICE
DANGER + SAFETY
CONTRACT + EXPAND
FAMOUS + UNKNOWN
DISTRIBUTE + GATHER
HORIZONTAL + VERTICAL
ACCIDENTAL + INTENTIONAL
IGNORANCE + KNOWLEDGE
Puzzle 7
A farmer has 5 haystacks in one field and 4 haystacks in the other field.
How many haystacks would there be if they were combined in one field?
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Puzzle 8
Can you find three consecutive odd numbers that …
… total 1,287 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
There are two different methods, one involves a cube root, and the other doesn't require a calculator.
Answer
9 x 11 x 13.
Reasoning #1
We're after three numbers that multiply together, so a good place to start is the cube root of 1,287, which is roughly 10.88.
Let's try dividing by the closest odd number to 10.88:
1287 ÷ 11 = 117
We're now after whole divisors of 117. Trying the odd numbers either side of 11 might work.
Trying either 9 or 13 gives the answer:
9 x 11 x 13 = 1,287
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Reasoning #2
We after three numbers that multiply together, but none of these can end in 5 (otherwise our answer would end in 0 or 5).
So, they can only end in 7, 9, 1 (e.g. 87, 89, 91), or 9, 1, 3 (e.g. 89, 91, 93).
However, if they ended in 7, 9, 1, the answer would end in 3 (because 7 x 9 x 1 = 63).
Therefore, they end in 9, 1, and 3 (because 9 x 1 x 3 = 27).
The first numbers we can try are 9, 11, 13:
= 9 x 11 x 13
= 99 x 13
= 100 x 13 − 13
= 1300 − 13
= 1,287
A calculator is not required!
