Solving clues
1-2-3 → one digit correct and in the right position.
4-5-6 → none correct.
1-4-7 → one digit correct but in the wrong position.
8-9-0 → none correct.
321
Three consecutive numbers have a sum of 75. What is the smallest number?
The smallest number is 24.
Find the next numbers:
3, 6, 18, 72, 360, ___
2160
(Multiply by 2, then 3, then 4, then 5, next multiply by 6)
Amy: “Brian did it.”
Brian: “Carl did it.”
Carl: “I didn’t do it.”
Only one is telling the truth. Who stole the test paper?
Carl stole the test paper.
If Brian is telling the truth, then Carl did it, which makes Amy and Carl’s statements false. Only Brian tells the truth.
I am a three-digit number.
My tens digit is four more than my ones digit.
My hundreds digit is three less than my tens digit.
The sum of my digits is 14.
What number am I?
473
2-3-3 → none right.
1-2-3 → one right and at the right position.
5-2-9 → one right and at the right position.
6-6-0 → one right and at the right position.
169
Austin scored 78 and 85 on his first two tests. What score does he need on the third test so his average is 87?
Austin needs to score a 98.
Find the next two numbers:
2, 3, 5, 9, 17, 33, ___, ___
65, 129
(Each term is previous term × 2 – 1:
Four people—Dan, Eva, Frank, and Gina—each make a statement about who took a cookie:
Dan: “Eva took it.”
Eva: “Frank took it.”
Frank: “Gina took it.”
Gina: “I didn’t take it.”
Only one person is telling the truth. Who took the cookie?
Gina took the cookie.
If Gina’s statement is true (“I didn’t take it”), then someone else did. But only one is telling the truth. Testing others shows only if Gina is lying and the others are false does it fit for Gina to have taken it.
I am a three-digit number.
My hundreds digit is twice my ones digit.
My tens digit is three less than my hundreds digit.
The sum of my digits is 17.
What number am I?
854
9-6-3 → none right.
5-2-0 → two right but not at the right position.
7-9-0 → none right.
2-4-7 → two right and at the right position.
245
If the side lengths of a triangle are three consecutive odd numbers, and the perimeter is 51 cm, what is the length of the longest side?
The longest side is 19 cm.
Find the next number in the sequence:
2, 5, 10, 17, 26, ___
37
The pattern is adding consecutive odd numbers:
2+3=5
5+5=10
10+7=17
...
At a contest, three contestants made these statements:
Helen: “I didn’t win.”
Ian: “Helen won.”
Jack: “Ian is lying.”
Only one of them is telling the truth. Who won?
Ian won.
If Ian tells the truth, Helen won, contradicting Ian winning. Testing possibilities shows Ian won fits only if Helen and Jack are lying.
My hundreds digit is half my tens digit plus 1.
My ones digit is 2 less than my hundreds digit.
The sum of my digits is 12.
What number am I?
462
9-2-4 → none right.
0-1-8 → one right and at the right position.
7-6-6 → one right but not at the right position.
7-8-9 → one right and at the right position.
688
The length of a rectangle is 3 cm less than twice its width. If the perimeter is 66 cm, what are the dimensions of the rectangle?
Width: 12 cm
Length: 21 cm
Find the next number in the sequence:
2, 4, 3, 6, 4, 8, ___
5
The sequence alternates between two simple rules:
Odd positions (1st, 3rd, 5th): increase by 1
2 → 3 → 4 → 5
Even positions (2nd, 4th, 6th): increase by 2
4 → 6 → 8
So, the 7th term follows the odd-position pattern: 4 → 5
Four students—Liam, Bella, Carlos, and Dana—are suspects. They say:
Liam: “Bella did it.”
Bella: “Dana didn’t do it.”
Carlos: “Bella is lying.”
Dana: “I didn’t do it.”
Exactly one statement is true. Who did it?
Dana. (Only Carlos’s statement is true; the others are false.)
I am a three-digit number.
My hundreds digit is half my tens digit plus 2.
My ones digit is 3 less than my hundreds digit.
The sum of my digits is 17.
What number am I?
683
8-6-7 → one right but not at the right position.
5-0-2 → none right.
7-3-7 → two right but not at the right position.
3-9-3 → two right and at the right position.
373
The sum of three consecutive multiples of 5 is 255. What are the numbers?
80, 85, 90
Find the next number in the sequence:
1, 11, 21, 1211, 111221, ___
312211
This is the famous “Look-and-say” sequence. Each term describes the digits of the previous term:
1 → "one 1" → 11
11 → "two 1s" → 21
21 → "one 2, one 1" → 1211
1211 → "one 1, one 2, two 1s" → 111221
111221 → "three 1s, two 2s, one 1" → 312211
Four friends — Nora, Owen, Paul, and Quinn — are suspects in a prank. They say:
Nora: “Paul did it.”
Owen: “Quinn did it.”
Paul: “Owen didn’t do it.”
Quinn: “Nora is lying.”
Exactly one of these statements is true. Who did the prank?
Owen did it.
If Owen did it, then Nora’s statement “Paul did it” is false, Owen’s “Quinn did it” is false, Paul’s “Owen didn’t do it” is false, and Quinn’s “Nora is lying” is true — exactly one truth.
I am a three-digit number.
My hundreds digit is one-third of the sum of my tens and ones digits.
My tens digit is two more than my ones digit.
The sum of my digits is 16.
What number am I?
475