September 2015 Logic & Maths Problems

1. cubefolding
The above net, consisting of orange, blue, red, yellow, pink and green squares can be folded to make a cubic box. Once assembled, which three pairs of colours will face opposite each other?

2. who's sitting where
Fred, Irene, Colin and Emily are sitting in a row but not in that order. Emily is not next to Fred or Irene. Fred is sitting on Irene’s immediate left as you look at them. Can you correctly work out who is sitting where?

3. washer A steel washer with a hole in the middle is heated until the metal expands evenly by 1 percent. Will the hole in the washer get larger, smaller, or remain the same size?

4. A darts player scored 91 with a treble, a double and a single (no bulls).
Given that the three numbers that he hits add up to 47 and that the difference between the largest and smallest of these three numbers is 5, how was this score made up?

5. necklace
A necklace is made up of five identical red beads and two identical green beads on a ring.
The ring is free to rotate, and the beads are free to slip around on the ring.
How many DIFFERENT such necklaces can be made using just five red beads and two green beads?

6. boat
A rowboat carrying a cannonball is floating in a swimming pool.
The cannonball is thrown overboard into the pool.
Will the water level in the pool
(a) Rise?
(b) Fall?
(c) Stay the same?

7. Can you find out what is unusual about this paragraph? It looks so ordinary that you might think that nothing is wrong with it. In fact, nothing is; but it is still an unusual sort of paragraph if you think about it. No doubt, if you work on it for about an hour it will dawn on you.

8. A player scores 75 with three darts, hitting a treble, a double and a single (no bulls).
Given that the three numbers that he hits add up to 35 and that the difference between the largest and smallest numbers is 14, how is this score made up?

9. A jailer has more than 1000 prisoners to guard and has to seat them at meal times according to the following rules:
• Each table is to seat the same number of prisoners.
• The number at each table is to be an odd number.
The jailer finds that when he seats the prisoners:
3 per table, he has 2 prisoners left over.
5 per table, he has 4 prisoners left over.
7 per table, he has 6 prisoners left over.
9 per table, he has 8 prisoners left over.
But when he seats 11 prisoners per table, there are none left over.
How many prisoners are there?

10. Applying a certain mathematical rule;
If you start with 10, you end up with 12.
If you start with 19, you end up with 30.
If you start with 23, you end up with 38.
Work out what the rule is, then using that rule, answer:
If you start with 14, what number will you end up with?


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