# Same Number Hunt

Used as Final Match of Season 3, Round 2, and Death Match of Season 4, Round 4.

Rules

Score points by correctly forming mathematical expressions resulting on the given number. Win by scoring 10 points first.

There is a grid of 16 letters. Behind each letter, there are the twelve numbers 1-12 and the four arithmetic operations +, -, ×, ÷. At the beginning, the back sides are shown for 5 seconds to the players, after which they are hidden again, only showing the letters. Then the game begins, playing round after round, until someone scores 10 points to be the winner.

In each round, a number is revealed; this number is a natural number that can be formed using the given numbers and operations. (For example, 23 can appear as 11+12 can be formed from the grid, but 29 will not appear.) A player that thinks they can form an equation should press the buzzer and recite three letters, corresponding to the numbers and operations. For example, if 11 is behind the letter C, + is behind the letter P, and 12 is behind the letter K, on a target number of 23 a player can recite CPK (or KPC) to score.

The expression must be in the form “number, operator, number”, and may not repeat any letter (thus 7+7 is not permitted). Upon pressing the buzzer, the player has 5 seconds to recite the expression, otherwise it’s considered as an incorrect answer. After reciting the letters, they are revealed; if the answer is incorrect, the turn is passed to the opposing player, who gets no time limit to form the equation. The turns are passed back and forth until a correct answer is made, which scores 1 point and begins the next round. The first player to score 10 points win the game.

As this is a Final Game, there are three items available (in addition to Item Copy and Item Disabler):

• Priority: Allows the user to answer the next round first without pressing the buzzer first. (This can only be activated at the start of a round, before the target number is revealed.)
• Double Chance: Allows the user to construct a 5-letter expression (number, operation, number, operation, number), which if correct, gives 2 points.
• Peek: Allows the user to check the back of one letter before answering.

In its reincarnation (season 4), there are no items. Additionally, subtraction is replaced by a special expression $\sqrt{x} + \sqrt{y}$, which takes the square roots of both operands and adds the results together. If one manages to complete an expression with this correctly, they score 2 points.

Discussion

(This discussion is initially made for the Final Match game (S3E12). I haven’t analyzed about its replay (S4E4).)

People cannot remember a lot of things at once, so the best strategy initially is to remember the most important things, the most important numbers and signs. But what are they?

First, division is worthless. Absolutely worthless. Subtraction works well enough to form small numbers (let’s say 1-7), addition for the middle numbers (8-20), and multiplication for the large numbers (21+).

And more, subtraction isn’t actually important, if one can memorize multiplication along with the number 1. Thus multiplication can cover the numbers 1-12, although this is not recommended; I’d say multiplication covers 1-4 along with 21+, and addition covers the rest (5-20).

If one doesn’t remember subtraction initially, they can look for the numbers 1, 2, 3 to cover the small numbers (1=1×1, 2=1×2, 3=1×3, 4=1+3, 5=2+3, 6=2×3), along with a few largish numbers to cover the middle range (perhaps 6, 7, 9, things like that). The largest numbers that can only be formed with multiplication has to wait, but now one can cover the small and middle numbers (let’s say 1-20) adequately with only around 7-8 things to remember.

If one decides to go to remember subtraction, now 1 is no longer necessary, at the expense of remembering four numbers. But these four can be middlish, like 2,3,5,7 (1=3-2, 2=5-3, 3=5-2, 4=7-3, 5=2+3, 6=2×3, 7=2+5, 8=3+5, 9=2+7, 10=3+7), so they can also help making up the middle and large range numbers.

Of course, the best strategy is to remember everything, but with only 5 seconds one can try to at least go for half of the grid, memorizing the rest as the game goes when they are used by the opponent.

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