What number should fill the empty square?
How you get the answer: The rightmost number in every row is calculated by multiplying second and third number on that row, then substracting the first number and adding the fourth. So, the answer is 3.
Can you fill the grid below with these blocks?
You can use every block as many times as you want. You can rotate blocks but not break them.
How you get the answer: This seems easy at first, but at the end of the day, blocks won’t fit. The reason behind that is that the grid has 14 × 5 = 70 squares in it, and all blocks have 4 squares. 70 isn’t divisible by 4, so the task is impossible.
What number should fill the empty triangle?
How you get the answer: There are three things that affect the number: Horizontal row, number of upward vertices and color. Here’s how it works: Horizontal row number (1…4 from up) × upward vertices (1 or 2) + color code (0…3)
For white, code is 0, light purple is 1, intermediate 2 and darkest 3. So the answer is 3×2+3=9.
Who is telling the truth?
From Alfie, Bert and Carl 1 is always lying, 1 is always truthful and 1 has truth and lies in his sentences.
A: C and I are telling the truth, B is lying
B: I’m telling the truth and others are not
C: We are all telling the truth
Who is who?
How you get the answer: Carl is saying “We are all telling the truth.” By definition, that can’t be the case. On the other hand, Alfie is saying that C is telling the truth, and so that can’t be right either. That leaves B is the truthteller. Now we can say that A is lying about himself, Bert and Carl so he is always lying. Carl is the one that has truth and lies in his sentences. What he says can be also stated mechanically as “A says the truth, B says the truth and C says the truth” and that is right only partially.
If 10 men will build a house in 10 days, how many houses will 50 men build in 50 days?
How you get the answer: Starting with the first part, if 10 men will build a house in 10 days, that means that 1 man will build that house in 100 days. (Yes, it would be difficult in real life but let’s just skip the real life here.) So, in the later case we have 50 × 50 = 2,500 man days which makes 2,500/100=25 houses.
Sum of 1, 2, 3, …, 1000?
How you get the answer:
1 + 1000 = 1001
This makes 500 × 1001 = 500,500
How you get 777 from digits?
Using digits 0, 1, 2, …, 9 and operators + – × ÷ how can you get number 777? You must use each digit exactly once. Operators can be used freely and brackets () are also in use.
How you get the answer: There are probably several ways to do this, but it’s wise to start thinking how you can get the result in the first place and worry about extra digits afterwards. Here is one solution:
768 + 9 = 777
96 × 8 + 9 = 777
32 × 3 × 8 + 9 = 777
(7 + 1) × 4 × 3 × 8 + 9 = 777
And finally, unused digits
(7 + 1) × 4 × 3 × 8 + 9 + 0 × (2 + 5 + 6) = 777
Replace each character with the right digit
How you get the answer: The $ sign has only two realistic options: 1 or 2. Since 2 seems more obvious, let’s try that first. If $ is 2 we can tell by the rightmost column that * is either 0 or 5. If it’s 0, then ? has to be 4. If it’s 5, then ? is 1. So possible answers are: $=2, *=0, ?=4 or $=2, *=5, ?=1.
Which number will replace the question mark?
How you get the answer: Every number in a circle is product of two primes. So there is one prime assigned to every line, and the final answer is seventy-seven.