You are given a 10x10x10 cube composed of one thousand 1x1x1 "mini-cubes" glued together. If the outer most layer falls off, how many "mini-cubes" would have fallen off?

[Ref: ZVPY]

Hint: Think about one face at a time.

Answer: 488.

You started with 10x10x10 = 1000 cubes. The outer layer falling off will leave you with 8x8x8 = 512 cubes, which means 488 cubes have fallen off.

Puzzle 408

A family photo contained:

one grandfather, one grandmother,
two fathers, two mothers,
six children, four grandchildren,
two brothers, two sisters,
three sons, three daughters,
one father-in-law, one mother-in-law, one daughter-in-law.

29 people you may think, but no! What is the fewest number of people that could have been in the photo?

Hint: A single member of the family can be both a sister and a daughter.

Answer: 8.

Four children (2 boys and 2 girls), their mother and father, the mother's mother, and the father's father.

Puzzle 409

Last weekend I travelled to my sister's house in Glasgow, around 250 miles away. I started on Saturday morning at 7am, traffic was heavy in places, and at times I was stationary. I arrived sometime after lunch.

On Sunday, it was time to make my way home, over exactly the same route. I left my sister's at exactly the same time, 7am, however, this time I came straight home without any travel delays, arriving home just before lunch.

How likely is it that I was at exactly the same point at exactly the same time on both days?

[Ref: ZGAI] Copyrighted.

Hint: It's more likely than you might first think.

Answer:
It's certain that I was in exactly the same place at exactly the same time on both trips.

This is perhaps easiest to see by asking my twin brother to make the return journey from Glasgow at the same time as I leave home on my way to Glasgow, on Saturday at 7am.

At some point during Saturday we will meet, and therefore be at the same place at the same time. The fact I did the return journey the following day does not change this.

Puzzle 410

Using the BrainTracker grid below, how many words can you find? Each word must contain the central P and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?