Puzzle of the Week #485 - Best Bet

I roll three standard dice, resulting in three random numbers between 1 and 6.

I bet you that you can’t make a number that is a multiple of ‘n’ by arranging the three numbers displayed on the dice to form a three-digit number.

‘n’ can be any ODD number larger than 1, which YOU nominate but you must do so BEFORE you see the results of the dice rolls.

For instance if you chose 13 and the dice rolls were 1, 6 and another 1, you could win by noting that 611 is a multiple of 13.

What is the best choice for ‘n’ to maximise your chances of winning?

Puzzle of the Week #484 - Twin Numbers

Consider a list of all of the three digit numbers that:

are a multiple of 4

contain three different digits

contain at least one odd digit

don’t contain a zero.

 

Prove that for every number that satisfies these criteria there is exactly one other that uses the same three digits in a different order and also satisfies the criteria.

 

 

 

Puzzle of the Week #483 - Trailing Zeroes

I have in mind a number, that is the smallest non-zero number that:

when doubled it is a square number,

when tripled it is a cube number,

when multiplied by 5 it is a power of 5, and

when multiplied by 7 it is a power of 7.

How many zeroes does it have after the last non-zero digit?

 

Although this puzzle might involve very large numbers, it can be approached without a computer or even a calculator.

Puzzle of the Week #482 - Number Triangle 2

Similar to last week, but now you have to arrange the numbers 1-15 in a triangle such that each number is the difference of the two numbers immediately below it.

This time there is only one possible solution (plus its reflection), but even if you cleverly narrow down the possibilities with a couple of quick observations, there are still over 60000 triangles to check without a computer.

Alternatively, if I were to give you the bottom row, completing the grid will be trivially easy.

In an effort to find a sweet spot, I have given you the numbers on the left hand slope. Some more numbers can be placed straight away, whereas others you can only initially narrow it down to a couple of possibilities.

Puzzle of the Week #480 - Wordle Cities

Presumably you’re familiar with the online game of Wordle but here’s a brief recap: you try to guess a solution word. If your guess word has any correct letters in the correct place they are coloured green. If your guess has correct letters but not in the correct place these are coloured yellow. If the solution word only has one E for instance, but your guess has two Es and neither are in the correct place, only the first will be coloured yellow.

 With that covered, I have come up with a variation. I have selected three English cities, and treated each of them as both the solution word and the guess word in all possible combinations, and coloured them according to Wordle rules. So for instance cities 2 and 3 start with the same letter, and cities 1 and 3 share a middle letter.

Your task is to identify the cities.

Puzzle of the Week #477 - Twenty Sum Thing

Fill in all the empty squares of the grid with the digits 1-9, such that:

 1:            A diamond shape denotes that the four numbers adjacent to it add to 20.

2:            Every diamond uses a different way to add to 20, so if for example one diamond is surrounded by 1,2,8,9, no other diamonds can use those same four numbers, not even in a different order.

3:            Identical digits are not allowed to occupy adjacent squares of the grid, not even diagonally adjacent.

Puzzle of the Week #475 - Letter Pairs

Use the following letter pairs to form a series of words: a 4-letter word, a 6-letter word, an 8-letter word, a 10-letter word and a 12-letter word.

Each of the letter pairs can only be used once, EXCEPT for five of them.

Those five special letter pairs appear at the end of each of the five words, and also earlier in the same word. For instance if the 8-letter word ends in OR, it would need to be either:

(OR----OR), (--OR--OR) or (----OROR).

 

AH  AM  BA  ID  IO  ME  NA  NC  NT  OR  OU  RA  SE  SY  TA

 

Puzzle of the Week #470 - Word List

The following words all have something specific in common:

SCAR   THOU  NAPA  SOLE   TECH  DOLL   DIVE    DIVE    GALA

The order they are in is related to the thing they have in common.

DIVE is in the list twice – this is not a mistake.

 Which one of the following words also belongs in the list, and where in the list should it be placed?

 BECK   CLEF   PARA   PAST