In the local wood there are a number of trees. On these trees there are a number of birds.
A local bird spotter knows that there are as many birds on each tree as there are trees in the wood, and that there are between 2,000 and 2,100 birds in total.
Reasoning
We are after a number whose square lies between 2,000 and 2,100.
45 is the only possible number.
??
Puzzle 2
Below you can find 8 words that have had their beginnings and endings removed. In each case, the same two letters can be found at the beginning and the end. For example REspiRE. --qui----yli----tat----gib----liv----rmi----ifi----alg--
Alex and Billie were rowing their canoe along the River Trent.
In the morning, they managed to row upstream at an average speed of 2 miles per hour.
They then stopped for a spot of lunch and a nice rest.
In the afternoon, the pace was a little easier as they were now rowing downstream back to their starting point, and managed an average speed of 4 miles an hour.
The morning trip took them 3 hours longer than the afternoon.
Hint
You can either fix the distance rowed and see what numbers work, or you can fix the number of hours.
Answer
12 miles.
In the morning, rowing at 2 miles per hour, they rowed for 6 hours. In the afternoon, rowing at 4 miles per hour, they rowed for 3 hours.
There are a number of ways of working this out, and here are two of them:
Method 1
If we assume the distance the rowed upstream to be D miles, we know the morning took (D ÷ 2) hours, and the afternoon took (D ÷ 4) hours, with a difference of 3 hours. So:
D D
- − - = 3
2 4
Multiplying throughout by 4 gives:
2D − D = 12
So:
D = 12 miles
They rowed 12 miles upstream.
Method 2
If we assume they rowed for H hours upstream, we know they travelled H x 2 miles in the morning. In the afternoon, they rowed for (H − 3) hours, and travelled (H − 3) x 4 miles. We know these distances are the same, so:
2H = (H − 3) x 4
Giving:
2H = 4H − 12
Rearranging gives:
12 = 2H
So:
H = 6 hours
They rowed for 6 hours upstream at 2 miles per hour, which is a total of 12 miles.
?
Puzzle 4
Start in the bottom left corner and move either up or right, one square at a time, using the numbers and the mathematical signs along the way. What is the largest total you can make?
+
2
−
4
+
2
2
+
2
−
2
+
−
1
+
3
−
3
2
−
3
+
1
−
+
1
−
3
+
2
3
+
3
−
2
+
Note: this puzzle is not interactive, and the numbers cannot be clicked.
