Reasoning There are 60 squares of size 1 x 1. There are 35 squares of size 2 x 2. There are 12 squares of size 3 x 3. There are 3 squares of size 4 x 4.
Giving a total of 60 + 35 + 12 + 3 = 110 squares.
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Puzzle 198
At a recent visit to the reptile house at the local animal sanctuary, I counted a total of 27 heads and 70 feet.
I was counting snakes, lizards, and people and I know that there were exactly twice as many lizards as people.
The total distance was 180 miles, but as I still had 5 miles to go, the required answer is 175 miles.
Reasoning
Let's try working backwards.
Day 4: I travelled 3/4, which means that the other 1/4 was 5 miles, and 20 miles were left at the start of day four.
Day 3: I travelled 2/3, which means that the other 1/3 was 20 mile, and 60 miles were left at the start of day three.
Day 2: I travelled 1/2, which means that the other 1/2 was 60 miles, and 120 miles were left at the start of day two.
Day 1: I travelled 1/3, which means that the other 2/3 was 120 miles, and 180 miles were ahead at the start of day one.
The full distance was therefore 180 miles, but we were asked how many miles I had travelled so far, and as I still had 5 to go the answer is 175 miles.
Double-Checking
Start distance: 180 miles.
Day 1: I travelled 1/3 of the distance (60 miles), leaving 120 miles.
Day 2: I travelled 1/2 of the distance (60 miles), leaving 60 miles.
Day 3: I travelled 2/3 of the distance (40 miles), leaving 20 miles.
Day 4: I travelled 3/4 of the distance (15 miles), leaving 5 miles.
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Puzzle 200
Starting with any number on the top row, make your way to the bottom, adding the numbers as you go.
Each time you must move to the next row, but you can move either straight down, or one place to the left or right.
What is the highest total you can make? What is the lowest?
1
5
1
5
1
5
3
3
2
3
3
4
2
3
4
4
3
2
2
2
3
2
2
4
2
2
4
3
4
2
4
4
4
4
2
3
Note: this puzzle is not interactive, and the numbers cannot be clicked.
