Each empty white square in the grid contains one of the numbers 1, 2, 3,..., 8. Each of the horizontal and vertical equations must be true and each number must be used exactly once.
[Ref: ZZVV] © Erich Friedman
Erich Friedman's Website.
Hint: The top-left square contains the 6.
Two friends were driving from their home to Manchester, Kevin drove the first 90 miles, and Daniel took over the remainder of the journey.
On the way back, Kevin drove to begin with, and Daniel took over for the last 100 miles.
Who drove the most?
[Ref: ZIMH] © Kevin Stone
Hint: It doesn't matter how far it was to Manchester.
On the way there Kevin drove 90 miles, and on the way back drove the (total distance - 100 miles).
On the way Daniel drove the (total distance - 90 miles), and on the way back drove 100 miles.
So Kevin drove 90 + total - 100 = total - 10.
And Daniel drove total - 90 + 100 = total + 10.
So Daniel drove 20 miles more than Kevin. QED.
Exactly how many minutes is it before seven o'clock, if 40 minutes ago it was three times as many minutes past two o'clock?
[Ref: ZNNB] © Kevin Stone
Hint: How many minutes are there between 2:00 and 7:00?
There are 300 minutes between 2:00 and 7:00 and we can ignore the "40 minutes ago" for a little while and share the remaining 260 minutes in the ratio 3:1, which is 195:65.
Which means the 5 hours between 2:00 and 7:00 are made of up 195 minutes + 40 minutes + 65 minutes.
Which means it is currently 65 minutes before 7:00. So it is now 5:55 (65 minutes before 7:00).
To double check, 40 minutes ago it was 5:15 - which is 195 minutes after 2:00, as required (as 65 x 3 = 195).
Moving up or right, what is the highest total you can make, using the mathematical signs along the way?
[Ref: ZDUC] © Kevin Stone
I recently went to the shop and purchased 4 items.
Three of the items cost:
There was quite a long queue, and as I was quite bored, I was playing with my pocket calculator whilst waiting.
Very curiously, the 4 prices added to the same number as I got when I multiplied the 4 prices together.
What was the price of the 4th item?
[Ref: ZAPY] © Kevin Stone
Hint: What do the 3 numbers add and multiply to give so far?
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.
The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.
You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.
The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
8.50 + P = 18.00 x P
8.50 = 18.00 x P - P
8.50 = 17.00 x P
8.50 ÷ 17.00 = P
P = 0.50. QED.