Maths Puzzles

Puzzle 1

Alan's son Daniel, is exactly one fifth of Alan's age.
In 21 years time, Alan will be exactly twice Daniel's age.
Betty's is exactly seven times the age of her daughter, Jessica.
In 8 years time, Betty will be three times the age of Jessica.
How old are Daniel and Jessica now?

[Ref: ZQZZ] © Kevin Stone

Hint: A little bit of algebra might help.

Answer: Daniel is 7 years old and Jessica is 4 years old.
The first half of the question involves Daniel (D) and Alan (A).
Daniel is currently one fifth of Alan's age, so:
A = D x 5 (1)
In 21 years time, Alan will be twice his age, so:
A + 21 = (D + 21) x 2 (2)
Using (1) in (2) gives:
A + 21 = (D + 21) x 2
5D + 21 = (D + 21) x 2
5D + 21 = 2D + 42
3D = 21
D = 7
So Daniel is 7 (and Alan is 35).
The second half of the question involves Jessica (J) and Betty (B).
Betty's is exactly seven times the age of Jessica:
B = J x 7 (3)
In 8 years time, Betty will be three times the age of Jessica, so:
B + 8 = (J + 8) x 3 (4)
Using (3) in (4) gives:
B + 8 = (J + 8) x 3
7J + 8 = (J + 8) x 3
7J + 8 = 3J + 24
4J = 16
J = 4
So Jessica is 4 (and Betty is 28). QED.

Puzzle 2

Complete this grid with the digits 1 to 6 to make the sum correct.
Perform each mathematical operation in the order shown, from left to right, e.g. 1 + 2 x 3 is treated as (1 + 2) x 3 = 9.
Note: there is no ÷ 1, and at no point is a decimal or fraction used.

[Ref: ZXLN] © Kevin Stone

Hint: The first number is 2.

Answer:

Puzzle 3

Within the BrainBashers school, the science department has three disciplines.
In total, 280 students study chemistry, 254 students study physics and 280 students study biology.
97 students study both chemistry and physics, 138 students study both physics and biology, 152 students study both chemistry and biology.
73 students study all three disciplines.
Can you determine how many students there are in the science department? The answer is well below 814.

[Ref: ZZYU] © Kevin Stone

Hint: How many students study chemistry and physics, but not biology?

Answer: 500 students.

The answer is most easily seen if three intersecting circles are drawn, and the numbers inside each section worked out.

Puzzle 4

What value of * makes the following correct:

[Ref: ZWPF] © Kevin Stone

Hint: The answer is a whole number less than 10.

Answer: 3.

Checking that 3 works:

3 3 3 3
- - - + - = -
3 2 4 12
1 - 1.5 + 0.75 = 0.25
0.25 = 0.25, which confirms that 3 is correct.
To deduce the answer directly from the question, we can multiply throughout by 12,
* * * *
- - - + - = -
* 2 4 12
to give:
12 - 6* + 3* = 1*
12 - 3* = 1*
12 = 4*
3 = *
As required.

Puzzle 5

Starting in the bottom left corner and moving either up or right, one square at a time, adding up the numbers along the way, what is the largest sum which can be made once you have reached the top right corner?

[Ref: ZNGR] © Kevin Stone

Hint: The answer is over 35.

Answer: 37.