Find three whole, positive numbers that have the same answer when multiplied together as when added together.
1,2, & 3
1 x 2 x 3 = 6 and 1 + 2 + 3 = 6
Ok, so there are 25 horses and the race track only allows 5 horses to race at a given time. Given that there is no stop watch available your task is to determine the fastest 3 horses. Assume that each horses speed is constant in different races, what is the minimum number of races to determine the fastest 3?
1. Divide the horses into five groups
2. Do another race with the horses that stood first of each group. Obviously, the winner in this race is the fastest.
3. Do one more race of the horses which stood 2nd and 3rd of the group of the fastest horse, 2nd and 3rd of the race in step 2, and the horse that stood second from the group 2nd of the heat in step 2.
From step 2, we know the fastest horse, and from step 3 the second and third fastest horses.
There are 9 similar balls. Eight of them weigh the same and the ninth is a bit heavier.
How would you identify the heavier ball if you could use a two-pan balance scale only twice?
Divide the 9 balls into 3 groups of 3. Weigh two groups. Thus you find out which group is the heavier ball in. Choose 2 balls from this group and compare their weights. And that's it.
Two men found a whole bag of sand gold (its not solid) treasure in the desert. Time came when they had to split thier ways and devide this whole bag. However, they dont have any kind of measuring equipment/tool. Nothing. Just 2 bags. (of course, one is full with sand gold)
How can they split it fairly so both parties agree on it and are happy about the split.
One will be in charge of splitting it in two portions, and the other will get to decide which portion he wants to keep. This will insure that the one in charge of splitting portions will do it as evenly as possible
they left the bag behind. that way it was split perfectly
I just found a number with an interesting property:
When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.
It's not a small number, but it's not really big, either. When I looked for a smaller number with this property I couldn't find one.
Can you find it?
Just take an LCM (least common multiple) of all the numbers in question and subtract 1 from it!
so the LCM of 2,3,4,5,6,7,8,9,10 = 8x9x7x5 = 2520
Hence, the solutions is 2519
Having 2 sandglasses: one 7-minute and the second one 4-minute, how can you correctly time 9 minutes?
T = 0min ---- Turn over the 4 and 7 minutes glasses.
T = 4min ---- The 4 runs out, Flip it. (3 minutes in 7 glass)
T = 7min ---- The 7 runs out, Flip it. (1 minute in the 4 glass)
T = 8min ---- The 4 runs out. 1 minute in bottom of 7 glass, Flip 7 glass.
T = 9min ---- The 7 runs out, 9 minutes reached +/- about 5 seconds to allow for flipping time.