Random Puzzles 

Workings

Hint
Adding just one should be enough.

Answer
Holes!

Workings

Hint
What are the maximum and minimum tonnes of pig feed I could have bought?

Answer
I bought 15 tonnes of chicken feed, 75 tonnes of pig feed, and 10 tonnes of cattle feed.

 15 x 0.15 =    2.25
 75 x 1.25 =   93.75
 10 x 0.40 =    4.00

100 tonnes = $100.00

A possible solution method follows …

I couldn't have bought 80 tonnes of pig feed because this would have cost the full $100.00, but I wouldn't have then had 100 tonnes in total.

Similarly, 70 tonnes of pig feed would have been too few, as this would cost $87.50 and even the remaining 30 tonnes all being cattle feed wouldn't have reached the required $100.00.

So, let's try 71 tonnes of pig feed = $88.75:

   plus 1 x chicken feed + 28 x cattle feed is over $100.00
   or   2 x chicken feed + 27 x cattle feed is under $100.00

   so 71 tonnes of pig feed doesn't work.

Let's try 72 tonnes … and so on.

We soon get to 75 tonnes of pig feed and find the answer.

Workings

Hint
It might be easier to find the S first.

Answer
Start with the P in the 5^th row, 6^th column:

Workings

Hint
Adding the speeds won't work.

Answer
205 mph.

Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.

The first ²/₅ are covered at 123 mph. Therefore, the time taken was [(²/₅) x L] ÷ 123 hours.

The next ²/₅ are covered at 164 mph. Therefore, the time taken was [(²/₅) x L] ÷ 164 hours.

The last ¹/₅ is covered at y mph. Therefore, the time taken was [(¹/₅) x L] ÷ y hours.

The entire trip is covered at an average of 150 mph, and we can conclude that:
 2L      2L      L     L
————— + ————— + ——— = ———
5x123   5x164    5y   150

Rearranging and simplifying gives:
 1     1    2     2
——— = —— - ——— - ———
 y    30   123   164

That means that y = 1 ÷ (¹/₃₀ − ²/₁₂₃ − ²/₁₆₄)

Using a calculator gives y = 205.