Skeptics Café

1. 18

2. Daniel is 7, Jessica is 4

3. 32
They change square colour when they move. So if they were all on the 32 white squares or the 32 black squares they could not attack each other.

4. 102 pages
To eat 300 pages with the books stacked as shown, the bookworm would have to eat from p100 Vol 1 to p1 vol 3

5. The red door
Process of elimination as follows:

6. a. 13; b. 18; c. 3

7. a

8. a. Keith b. first c. Adrian

9. 2/3 (not 1/2)

You know that you do not have Bag B (two black marbles) so there are three possibilities

You chose Bag A, first white marble. The other marble will be white
You chose Bag A, second white marble. The other marble will be white
You chose Bag C, the white marble. The other marble will be black

So 2 out of 3 possibilities are white.

Why not 1/2? You are selecting marbles, not bags.

10. 125 m³..

(half as high means all three dimensions are in the ratio 0.5.

The smaller pyramid’s volume is

0.5 × 0.5 × 0.5 = 0.125

 that of the larger pyramid.)

1. 6

2. 12

3. 44 years.

Let the number of years elapsed on the lease be y.
Then the number of years left on the lease is (99-y).

3y / 4   =  3(99-y) / 5

15y = 12(99-y)

15y = 1188 – 12y

27y = 1188

y = 44

4. “You forgot the spaces between ‘Johnson’ and ‘and’ and ‘and’ and ‘Smith’ ”

5. 720 times

6. 2 cakes

7. 60 legs
For any centipede to have the largest possible number of legs means the largest possible share of the available 122 legs.
Obviously this implies only one centipede. That leaves 10 heads shared between spiders and ants. Since spiders have more legs than ants, we are looking for the least possible number of spiders (1) hence 9 ants.
1 spider and 9 ants account for (8 + 54) = 62 legs. That leaves 60 legs available to the centipede.

8. Carrots $2.99, spring onions $1.99, parsnips $5.99

9. A = 8 B =2 C=1

111A+111B+111C=110B+1001C which reduces to
111A+B=890C

The most 111A can be is 999 so the most (111A + B) can be is 999 + 8 = 1007.
So C can only be 1. For example, if C was 2, 890C would be 1780.
Therefore 111A+B=890

A must be 8 for the equality to be possible,

=> B=2

10. 1009

A possible way of approaching the problem is as follows:
a. Eliminate even numbers.
b. Eliminate numbers ending in 5.
c. Eliminate numbers using the “divisible by 3” rule. Any whole number which is divisible by 3 has digits which add up to a multiple of 3
d. Of the remaining possibilities (1001, 1003, 1007, 1009, 1013, 1019, ………..) begin with the lowest and attempt to divide by successive primes beginning with 7. You can stop when you get to a square root. As 31 squared is 961 and 37 squared is 1361, that effectively means if you get to 31 in your attempt to divide by successive primes you’ve gone far enough.
1001 = 7 X 143 = 7 X 11 X 13 NOT PRIME
1003 is not divisible by 7, 11, or 13. However it is divisible by 17.
1003 = 17 X 59 NOT PRIME
1007 is not divisible by 7, 11, 13 or 17. However it is divisible by 19
1007 = 19 X 53 NOT PRIME
1009 is not divisible by 7, 11, 13, 17, 19, 23, 29 or 31. It is therefore PRIME.

1. The Philistines

2. 1890s, 1930s

3. B. clever

4. Stalactites hang down. Stalagmites stick up.

5. Naples

6. Paul VI, John Paul I, John Paul II

7. B. Part of a horse’s foot

8. One of Australia’s two active volcanos, it erupted and doubled its size

9. The Dig Tree of the Burke and Wills Expedition

10. Everyone

HARDER:

11. The first international website

12. Earl of Pembroke

13. Iodine

14. Yellow

15. New South Wales. Its platypus is a monotreme

16. Surveying

17. Nepal (5¾ hours ahead of GMT)

18. They’re all dead. (It’s in the Southern Hemisphere’s largest cemetery complex)

19. HMS ENDEAVOUR

20. Win gold medals (in different sports) in both the Summer and Winter Olympics

1. 120

2. Jo is Number 1, Mary is Number 2, Beth is Anchor

3. He’s lying.

“To deny the opposite of the veracity” = to deny falsehood = to affirm the truth

“I guarantee that it is untenable” = it cannot be maintained

4. MDCLXVI = 1666

5. 364

6. $188.85 ($100 + $50 + $10 + $5 + $2 + $1 + 50c + 20c + 10c + 5c)

7. 11

8. 45 pencils, 11 jars

9. 18 km

10. C

1. Ramparts
2. Expert panel
3. Easy on the eye
4. French polish
5. Towering Inferno
6. Gone With the Wind
7. Pale Rider