Hint
What must the middle temperature be? Remember that the temperature are in degrees Celsius.
Answer
The temperatures were -6, -2, 2, 6, 10 °C.
Each day increased by a steady 4 degrees.
Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).
Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).
If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.
If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does matches all of the requirements.
If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.
Any larger increase makes the product even larger, so we can stop checking.
So the only possible answer is -6, -2, 2, 6, 10.
?
Puzzle 395
If cat and a half can catch a mouse and a half in a day and a half how many mice can 3 cats catch in 3 days?
The four clowns in this puzzle all competed for the much-prized 'Clown of the Year' award recently. There were 30 clowns in total who entered the competition and each had to make the judges laugh.
From the clues below, can you work out each clown's name, the town he or she came from, what place each clown was awarded and the most comical moment of each clown's routine?
The Budsworth clown finished one place lower than Strumpy who is not from Witfield. The judges roared with laughter as one clown cycled across a tightrope, wobbled, screamed and fell head first into a pool of water. He finished two places below Boo Boo who was not from Witfield. The clown who finished in 7th place lost points when her big red nose fell off during her manic routine. This involved being hit with a giant rubber mallet by her assistant who was supposed to hit her on the shoulder but unfortunately had something in his eye at the time and accidentally hit her in the face instead. Tambo was disappointed when his usually masterful custard pie antics failed to impress the judges sufficiently to secure the award. He was not the clown from Stockville whose final placing was lower than the Shrimpton clown.
Clowns : Boo Boo, Grego, Strumpy, Tambo
Towns : Budsworth, Shrimpton, Stockville, Witfield
Position : 2nd, 4th, 5th, 7th
Routine : Custard Pie, Flower, Rubber Mallet, Unicycle
Answer Name Town # Routine Boo Boo Shrimpton 2nd Flower Strumpy Stockville 4th Unicycle Tambo Budsworth 5th Custard Pie Grego Whitfield 7th Rubber Mallet
The positions that the four clowns could finish are 2nd, 4th, 5th and 7th. The Budsworth clown finished one place below Strumpy (1) so Strumpy must have been 4th and the Budsworth clown 5th. The (male) clown on the unicycle finished two places below Boo Boo (2) so must have been 7th or 4th. Since the clown who came 7th was female, the clown on the unicycle must have been 4th and is Strumpy and Boo Boo came 2nd. Tambo (male) is not the clown who came 7th (3), 2nd (Boo Boo) or 4th (Strumpy) so came 5th with his custard pie act (4) and Grego came 7th with her rubber mallet so by elimination, Boo Boo's act involved the flower. The Budsworth clown (Tambo) came 5th, neither Strumpy (1) nor Boo Boo (2) came from Whitfield so the clown from Whitfield was Grego (7th). The Shrimpton clown was placed higher than the Stockville clown (4) so came 2nd and the Stockville clown came 4th.
