1.) Grandma takes five minutes to climb from the first floor of the building to the fifth. If she climbs at the same speed, how long will it take her to reach the ninth floor from the first?

2.) Juan and Candice are using a spring scale to weigh their book bags. When they are weighed separately, the scale shows 3lbs and 2lbs. When they weight them together, the scale shows 6lbs.
"That can't be right," said Candice. "Two plus three doesn't equal six!"
"Don't you see?" answered Juan. "The pointer on the scale is off."
How much do the book bags actually weigh?

3.) Use the fingers of one hand to count as follows: the thumb is first, the index finger is second, and so on to the pinkie which is fifth. Then reverse direction so that the ring finger is sixth, the middle finger is seventh, the index finger is eighth, and the thumb is ninth. Reverse direction again back toward the pinkie with the index finger tenth, and so on. If you continue to count back and forth along the fingers of one hand, which finger will be the 1000th one?

4.) A dot is marked in a circle. (a) Cut the circle into at most three parts so that, by rearranging the parts, you get a circle with its center at the dot. (b) is it possible to do so by cutting the circle into at most two parts?

5.) A brother leaves his house 5 minutes after his sister. If he walks at 1.5 times her speed, how long will it take him to catch up?

6.) The diagram shows the rolling track of a bulldozer, seen from the side. The bottom is in contact with the ground. If the bulldozer moves forward 10cm, how many centimeters does the point marked A move?

7.) Together Winnie the Pooh, Owl, Rabbit, and Piglet ate 70 bananas. Each ate a whole number of bananas, and each ate at least one. Pooh ate more than each of the others; Owl and Rabbit together ate 45 bananas.How many bananas did Piglet eat?

8.) While walking in the park, Nicole and Valerie came to a large round clearing surrounded by a ring of cottonwood trees and decided to count trees. Nicole walked around the clearing and counted all of the trees. Valerie did the same, but started from a different tree. Nicole's 20th tree was Valerie's 7th, while Nicole's 7th tree was Valerie's 94th. How many trees were growing around the clearing?

9.) A group from a summer camp leaves a forest where they have been gathering flowers. They walk in boy-girl pairs, and in each pair the boy has either three times as many or one third as many flowers as the girl has. Is it possible for the whole group to have 2006 flowers?

***I have solved 7 of the 9, but i wont tell you which ones!***
I think I've solved them all. Should I post solutions or not spoil the answers?
lirtosiast wrote:
I think I've solved them all. Should I post solutions or not spoil the answers?

flip them upside down!
lirtosiast wrote:
I think I've solved them all. Should I post solutions or not spoil the answers?

You can PM them to me Smile i am interested to see what other people thought about them Razz
I solved them all as well Smile
Are we allowed to post some of our own?

Cuz I have a few I'd like to share Smile.

EDIT: Here's one!

With 5 eight's, and 5 basic operators (+, -, *, /, ^, plus parenthesis, of course.), is it possible to get the numbers 1 - 16 (It may be no, 16 is arbitrary Wink)?
If so: how, and how far can you go (continuously after 10)?

(8/8)^8-(8/8) = 0

jonbush asked a very good question:
jonbush wrote:
So we must use all five 8's, but we can use any number of operators?


And no programs to try every single combo, either. Fine... I used one myself to solve it anyway...

And if you do create a program, you need to explain (prove, in short) why that particular one is impossible... Evil or Very Mad

Hints (filthy cheater Razz):

Hint #1
Hint #2
Sure! I don't care Razz
There we go, I've checked every number upto 50, the ones that are not in the list are not possible.

1: (8-8)*8+8/8
2: (8+8)/(8*8/8)
3: 8/8+(8+8)/8
4: (8+8+8+8)/8
5: 8-(8+8+8)/8
6: (8*8-8-8)/8
7: 8*8/8-8/8
8: 8*8*8/8/8
9: 8*8/8+8/8
10: (8*8+8+8)/8
11: 8+(8+8+8)/8
12: 8+8*8/(8+8)

14: 8+8-(8+8)/8
15: 8+8-(8/8)^8
16: (8*8)/((8+8)/8)
17: 8+8+(8/8)^8
18: 8+8+(8+8)/8

23: 8+8+8-8/8
24: 8+8+8+8-8
25: 8+8+8+8/8

32: (8+8)*(8+8)/8

40: 8+8+8+8+8

48: 8*(8-8/8)-8
Correct! Good job! I got another one, and it's even more tedious.

If you have 4 of the numbers 1 - 9 (excluding 4, that makes this pointless), and you can only use one of the same type per equation, what numbers can you NOT express using only:

(), +, - (or negative), /, ^, sqrt(), nth-root(), and factorial
1-200 is required, but -500 to 500 for brownie points! (yay)

I tested this out, and it is rather cool.

Okay, today I work I got a really fun math questions, and I weren't be able to solve it.
Say you get a bunch of numbers, and it produces a special checksum, from 0-9 based on that number. It's known there is a certain algorithm behind it, to produce that checksum, but I dunno what. Can you guys help me solving it? Smile


73638 -> 9
82445 -> 8
81245 -> 3
79968 -> 4
84977 -> 8
84969 -> 5
84961 -> 2
84954 -> 7
84944 -> 8
84882 -> 0
84836 -> 6
84834 -> 1
84754 -> 1
60000 -> 7
60001 -> 5
60002 -> 3
60003 -> 1
60004 -> 9
60005 -> 6
60006 -> 4
60007 -> 2
60008 -> 0
60009 -> 8
60010 -> 6

Based on the last series, I was something like "when the input increments one, the checksum decreases with 2, and if the last digit from the input goes from 4->5, it decreases once more". Applying that to 84944 and 84954 confirms it, but from 84834 to 84944 fails.
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